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PRACTICAL CONVERSION OF ZERO-POINT ENERGY
FEASIBILITY STUDY
OF ZERO-POINT ENERGY EXTRACTION
FROM THE QUANTUM VACUUM FOR THE PERFORMANCE OF USEFUL WORK
Now with “Vacuum Engineer’s Toolkit” – Table 3 – p. 74
Revised Edition, 2005
By
Thomas Valone, Ph.D., P.E.
Drawing courtesy of Science News
Integrity Research Institute
5020 Sunnyside Ave, Suite 209
Beltsville MD 20705
1
PRACTICAL CONVERSION OF ZERO-POINT ENERGY
Feasibility Study of Zero-Point Energy Extraction from the Quantum Vacuum for the
Performance of Useful Work
Thomas Valone, PhD, PE
ISBN 0-9641070-8-2
Copyright © 2003 Thomas Valone
Second Edition, 2004
Third Edition, 2005
Integrity Research Institute, 5020 Sunnyside Avenue - Suite 209, Beltsville MD 20705
Phone 301-220-0440, 800-295-7674
A nonprofit 501(c)3 organization
www.IntegrityResearchInstitute.org
This study is also summarized in a 90-minute lecture & slide presentation on DVD from the
Institute for New Energy Conference, Salt Lake City, 2004, “Zero Point Energy Extraction from
the Quantum Vacuum.” The IRI #821 is DVD only and $10 off for owners of this study when
you order online or by phone to Integrity Research Institute. Alternatively, Lost Arts Media
(800-952-LOST) has either VHS or DVD of the Valone lecture on zero-point energy from 2004.
The first edition of this study was a dissertation presented to the faculty of the School of
General Engineering at Kennedy-Western University in partial fulfillment for the degree of
Doctor of Philosophy in General Engineering on September 30, 2003.
Order Zero-Point Energy: The Fuel of the Future – a popular book for everyone by Dr. Valone
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TABLE OF CONTENTS
TABLE OF CONTENTS............................................................................................................. 3
PREFACE to Revised Edition.................................................................................................... 5
CHAPTER 1 - Introduction....................................................................................................... 6
Zero-Point Energy Issues ................................................................................................... 6
Fluctuation-Dissipation Theorem ...................................................................................... 11
Statement of the Problem ................................................................................................. 12
Purpose of the Study ........................................................................................................ 13
Importance of the Study ................................................................................................... 13
Rationale of the Study ...................................................................................................... 15
Definition of Terms ........................................................................................................... 15
Overview of the Study ...................................................................................................... 16
CHAPTER 2 - Review of Related Literature ............................................................................ 17
Historical Perspectives ..................................................................................................... 17
Casimir Predicts a Measurable ZPE Effect....................................................................... 18
Ground State of Hydrogen is Sustained by ZPE............................................................... 19
Lamb Shift Caused by ZPE .............................................................................................. 19
Experimental ZPE............................................................................................................. 20
ZPE Patent Review .......................................................................................................... 20
ZPE and Sonoluminescence ............................................................................................ 21
Gravity and Inertia Related to ZPE ................................................................................... 22
Heat from ZPE.................................................................................................................. 22
Summary .......................................................................................................................... 23
CHAPTER 3 - Methodology..................................................................................................... 24
Approach .......................................................................................................................... 24
What is a Feasibility Study?.............................................................................................. 24
Data Gathering Method .................................................................................................... 25
Database Selected for Analysis........................................................................................ 25
Analysis of Data................................................................................................................ 25
Validity of Data ................................................................................................................. 25
Uniqueness and Limitations of the Method....................................................................... 25
Summary .......................................................................................................................... 26
CHAPTER 4 - Analysis ............................................................................................................ 27
Introduction to Vacuum Engineering................................................................................. 27
Electromagnetic Zero-Point Energy Converter ................................................................. 27
Microsphere Energy Collectors......................................................................................... 31
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Nanosphere Energy Scatterers ........................................................................................ 35
Picosphere Energy Resonators ........................................................................................ 37
Quantum Femtosphere Amplifiers .................................................................................... 40
Deuteron Femtosphere..................................................................................................... 42
Electron Femtosphere ...................................................................................................... 43
Casimir Force Electricity Generator.................................................................................. 44
Cavity QED Controls Vacuum Fluctuations ...................................................................... 47
Spatial Squeezing of the Vacuum..................................................................................... 48
Focusing Vacuum Fluctuations......................................................................................... 49
Stress Enhances Casimir Deflection ................................................................................ 49
Casimir Force Geometry Design ...................................................................................... 50
Vibrating Cavity Photon Emission..................................................................................... 53
Fluid Dynamics of the Quantum Vacuum ......................................................................... 54
Quantum Coherence Accesses Single Heat Bath ............................................................ 56
Thermodynamic Brownian Motors .................................................................................... 58
Transient Fluctuation Theorem......................................................................................... 61
Power Conversion of Thermal Fluctuations ...................................................................... 62
Rectifying Thermal Noise with Ratchets ........................................................................... 63
Ferrofluid Thermal RecifierTorque Engine........................................................................ 64
Rectifying Thermal Electric Noise..................................................................................... 65
Quantum Brownian Nonthermal Recifiers without Ratchets ............................................. 65
Zero Point Energy Corresponds to Dark Energy .............................................................. 67
Vacuum Field Amplification .............................................................................................. 67
CHAPTER 5 - Summary, Conclusions and Recommendations............................................... 68
Summary .......................................................................................................................... 68
Electromagnetic Conversion............................................................................................. 68
Mechanical Casimir Force Conversion ............................................................................. 70
Fluid Dynamics ................................................................................................................. 70
Thermodynamic Conversion............................................................................................. 70
Conclusions ...................................................................................................................... 72
Recommendations............................................................................................................ 73
Table 3 - Vacuum Engineer’s Toolkit ..................................................................................... 74
FIGURE CREDITS .................................................................................................................. 76
REFERENCES ........................................................................................................................ 79
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PREFACE to Revised Edition
Today this country faces a destabilizing dependency on irreplaceable fossil fuels which are also
rapidly dwindling. As shortages of oil and natural gas occur with more frequency, the “New Energy
Crisis” is now heralded in the news media.1 However, an alternate source of energy that can replace
fossil fuels has not been reliably demonstrated. A real need exists for a portable source of power
that can compete with fossil fuel and its energy density. A further need exists on land, in the air,
and in space, for a fueless source of power which, by definition, does not require re-fueling. The future
freedom, and quite possibly the future survival, of mankind depend on the utilization of such a source of
energy, if it exists.
However, ubiquitous zero-point energy is known to exist. Yet, none of the world’s physicists or
engineers are participating in any national or international energy development project, such as
advocated by the Apollo Alliance, that would extend beyond nuclear power. It is painfully obvious that
zero-point energy does not appear to most scientists as the robust source of energy worth developing.
Therefore, an aim of this study is to provide a clear understanding of the basic principles of the only
known candidate for a limitless, fueless source of power: zero-point energy. Another purpose is to look
at the feasibility of various energy conversion methods that are realistically available to modern
engineering, including emerging nanotechnology, for the possible use of zero-point energy.
To accomplish these proposed aims, a review of the literature is provided, which focuses on the
major, scientific discoveries about the properties of zero-point energy and the quantum vacuum.
Central to this approach is the discerning interpretation of primarily physics publications in the light of
mechanical, nuclear, thermal, electronic and electrical engineering techniques. Applying an engineering
analysis to the zero-point energy literature places more emphasis the practical potential for its energy
conversion, especially in view of recent advances in nanotechnology.
With primary reference to the works of H. B. G. Casimir, Frank Mead, Fabrizio Pinto, and Peter
Milonni, key principles for the proposed extraction of energy for useful work are identified and analyzed.
These principles fall into the thermodynamic, fluidic, mechanical, and electromagnetic areas of
primary, forcelike quantities that apply to all energy systems. A search of zero-point energy
literature reveals that these principles also apply to the quantum level. Chapter 4 begins the Analysis
section with the Frank Mead patent as the Electromagnetic Zero-Point Energy Converter from
pages 27 – 44. The rest of the examples are much more brief, such as the Pinto patent Casimir Force
Electricity Generator analysis from pages 44 – 50. Though the Mead analysis contains valuable
comparisons of four different sphere sizes, it is the most technical physics in the study and may be
skipped over for the first reading through, without loss of continuity.
The most feasible modalities for the practical conversion of zero-point energy into useful work,
such as the fluctuation-driven transport of an electron ratchet, the quantum Brownian nonthermal
rectifiers, and the Photo-Carnot engine are also explored in more detail. One-liner, boldface key
sentences appear throughout the study for emphasis of the most important discoveries in the field.
Specific suggestions for further research in this area conclude this feasibility study with a detailed
section devoted to summary, conclusions and recommendations. For a less technical overview, my
ZPE lecture DVD is highly recommended as well as the forthcoming book, Zero-Point Energy: the Fuel
of the Future. A Definition of Terms appears on pages 15-16, Vacuum Engineer’s Toolkit on page 74.
Thomas Valone
Washington DC
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CHAPTER 1 - Introduction
Zero-Point Energy Issues
Zero-point energy (ZPE) is a universal natural phenomenon of great significance which has
evolved from the historical development of ideas about the vacuum. In the 17th century, it was thought
that a totally empty volume of space could be created by simply removing all gases. This was the first
generally accepted concept of the vacuum. Late in the 19th century, however, it became apparent that
the evacuated region still contained thermal radiation. To the natural philosophers of the day, it seemed
that
all
of
the
radiation
might
be
eliminated
by
cooling.
NASA: www.grc.nasa.gov
Figure 1
Thus evolved the second concept of achieving a real vacuum: cool it down to zero temperature after
evacuation. Absolute zero temperature (-273C) was far removed from the technical possibilities of that
century, so it seemed as if the problem was solved. In the 20th century, both theory and experiment
have shown that there is a non-thermal radiation in the vacuum that persists even if the temperature
could be lowered to absolute zero. This classical concept alone explains the name of "zero-point"
radiation2.
In 1891, the world’s greatest electrical futurist, Nikola Tesla, predicted the existence of zeropoint energy by stating, “Throughout space there is energy. Is this energy static or kinetic? If static our
hopes are in vain; if kinetic – and we know it is, for certain – then it is a mere question of time when
men will succeed in attaching their machinery to the very wheelwork of Nature. Many generations may
pass, but in time our machinery will be driven by a power obtainable at any point in the
Universe.”3
7
“From the papers studied the author has grown increasingly convinced as to the relevance of
the ZPE in modern physics. The subject is presently being tackled with appreciable enthusiasm and it
appears that there is little disagreement that the vacuum could ultimately be harnessed as an energy
source. Indeed, the ability of science to provide ever more complex and subtle methods of harnessing
unseen energies has a formidable reputation. Who would have ever predicted atomic energy a century
ago?”4
A good experiment proving the existence of ZPE is accomplished by cooling helium to within
microdegrees of absolute zero temperature. It will still remain a liquid. Only ZPE can account for the
source of energy that is preventing helium from freezing.5
Besides the classical explanation of zero-point energy referred to above, there are rigorous
derivations from quantum physics that prove its existence. “It is possible to get a fair estimate of the
zero point energy using the uncertainty principle alone.”6 As stated in Equation (1), Planck’s constant h
(6.63 x 10-34 joule-sec) offers physicists the fundamental size of the quantum. It is also the primary
ingredient for the uncertainty principle. One form is found in the minimum uncertainty of position x and
momentum p expressed as
Δx Δp > h/4π
(1)
In quantum mechanics, Planck’s constant also is present in the description of particle motion.
“The harmonic oscillator reveals the effects of zero-point radiation on matter. The oscillator consists of
an electron attached to an ideal, frictionless spring. When the electron is set in motion, it oscillates
about its point of equilibrium, emitting electromagnetic radiation at the frequency of oscillation. The
radiation dissipates energy, and so in the absence of zero-point radiation and at a temperature of
absolute zero the electron eventually
comes to rest. Actually, zero-point
Figure 2
radiation continually imparts random
impulses to the electron, so that it never
comes to a complete stop (as seen in
Figure 2). Zero-point radiation gives the
oscillator an average energy equal to the
frequency of oscillation multiplied by onehalf of Planck's constant.”7
However, a question regarding
the zero-point field (ZPF) of the vacuum
can be asked, such as, “What is
oscillating and how big is it?” To answer
this, a background investigation needs to
be done. The derivation which follows uses well-known physics parameters. It serves to present a
conceptual framework for the quantum vacuum and establish a basis for the extraordinary nature of
ZPE.
In quantum electrodynamics (QED), the fundamental size of the quantum is also reflected in the
parton size. “In 1969 Feynman proposed the parton model of the nucleon, which is reminiscent of a
model of the electron which was extant in the late 19th and early 20th centuries: The nucleon was
assumed to consist of extremely small particles—the partons—which fill the entire space within a
nucleon. All the constituents of a nucleon are identical, as are their electric charges. This is the simplest
parton model.”8
The derivation of the parton mass gives us a theoretical idea of how small the structure of the
quantum vacuum may be and, utilizing E = mc2, how large ZPE density may be. For convenience, we
substitute h = “hbar“ = h/2π for which the average ZPE = ½ hf = ½ hω, since the angular frequency ω =
2πf.
8
The Abraham-Lorentz radiation reaction equation contains the relevant quantity, since the
radiation damping constant Γ for a particle’s self-reaction is intimately connected to the fluctuations of
the vacuum.9 The damping constant is
Γ = 2 e2 / 3 moc3
(2)
10
where mo is the particle mass. It is also known in stochastic electrodynamics (SED) that the radiation
damping constant can be found from the ZPE-determined inertial mass associated with the parton
oscillator.11 It is written as
Γ = π mo c2 / hωc2
(3)
Here ωc is the zero-point cut-off frequency which is regarded to be on the order of the Planck cut-off
frequency (see eq. 8), given by
ωC =
π c5
hG
(4)
Equating (2) and (3), substituting Equation (4) and rearranging for mo gives
mo = e
2
3G
(5)
Therefore, the parton mass is calculated to be
mo ≈ 0.16 kg
(6)
For comparison, the proton rest mass is approximately 10-27 kg, with a mass density of 1014 g/cc.
Though “it might be suggested that quarks play the role of partons” the quark rest mass is known to be
much smaller than loosely bound protons or electrons.12 Therefore, Equation (6) suggests that partons
are fundamentally different.
The answer to the question of how big is the oscillatory particle in the ZPF quantum vacuum
comes from QED. “The length at which quantum fluctuations are believed to dominate the geometry of
space-time” is the Planck length:13
Planck length =
Gh
≈ 10 − 35 m
3
2πc
(7)
The Planck length is therefore useful as a measure of the approximate size of a parton, as well as “a
spatial periodicity characteristic of the Planck cutoff frequency.”14 Since resonant wavelength is
classically determined by length or particle diameter, we can use the Planck length as the wavelength λ
in the standard equation relating wavelength and frequency,
c = f λ = ωc λ /2π
(8)
and solving for ωc to find the Planck cutoff frequency ωc ≈ 1043 Hz.15 This value sets an upper limit on
design parameters for ZPE conversion, as reviewed in the later chapters. Taking Equation (6) divided
by Equation (7), the extraordinary ZPF mass density estimate of 10101 g/cc seems astonishing, though,
like positrons (anti-electrons), the ZPF consists mostly of particles in negative energy states. This
derived density also compares favorably with other estimates in the literature: Robert Forward
9
calculates 1094 g/cc if ZPE was limited to particles of slightly larger size, with a ZPF energy density of
10108 J/cc.16 (NASA has a much smaller but still “enormous” estimate revealed in Figure 1.)
Another area of concern to the origin of the theoretical derivation of ZPE is a rudimentary
understanding of what meaning Planck attributed to “the average value of an elementary radiator.”17
“The absorption of radiation was assumed to proceed according to classical theory, whereas emission
of radiation occurred discontinuously in discrete quanta of energy.”18 Planck’s second theory,
published in 1912, was the first prediction of zero-point energy.19 Following Boltzmann, Planck looked
at a distribution of harmonic oscillators as a composite model of the quantum vacuum. From
thermodynamics, the partial differential of entropy with respect to potential energy is ∂S/∂U = 1/T. Max
Planck used this to obtain the average energy of the radiators as
U = ½hf + hf /(e hf/ kT – 1)
(9)
where here the ZPE term ½hf is added to the radiation law term of his first theory.
Using this equation, “which marked the birth of the concept of zero-point energy,” it is clear that
as absolute temperature T Æ 0 then U Æ ½hf, which is the average ZPE.20
Interestingly, the ground state energy of a simple harmonic oscillator (SHO) model can also be
used to find the average value for zero-point energy. This is a valuable exercise to show the
fundamental basis for zero-point energy parton oscillators. The harmonic oscillator is used as the model
for a particle with mass m in a central field (the “spring” in Figure 2). The uncertainty principle provides
the only requisite for a derivation of the minimum energy of the simple harmonic oscillator, utilizing the
equation for kinetic and potential energy,
E = p2/2m + ½ m ω2 x2 .
(10)
Solving the uncertainty relation from Equation (1) for p, one can substitute it into Equation (10).
Using a calculus approach, one can take the derivative with respect to x and set the result equal to
zero. A solution emerges for the value of x that is at the minimum energy E for the SHO. This x value
can then be placed into the minimum energy SHO equation where the potential energy is set equal to
the kinetic energy. The ZPE solution yields ½hf for the minimum energy E.21
This simple derivation reveals the profoundly fundamental effect of zero-point radiation on
matter, even when the model in only a SHO. The oscillator consists of a particle attached to an ideal,
frictionless spring. When the parton is in motion, it accelerates as it oscillates about its point of
equilibrium, emitting radiation at the frequency of oscillations. The radiation dissipates energy and so in
the absence of zero-point radiation and at a temperature of absolute zero the particle would eventually
comes to rest. In actuality, zero-point radiation continually imparts random impulses to the particle so
that it never comes to rest. This is Zitterbewegung motion. The consequence of this Zitterbewegung
is the averaged energy of Equation (15) imparted to the particle, which has an associated long-range,
van der Waals, radiation field which can even be identified with Newtonian gravity. Information on this
discovery is reviewed in Chapter 2.
In QED, the employment of perturbation techniques amounts to treating the interaction between
the electron and photon (between the electron-positron field and the electromagnetic field) as a small
perturbation to the collection of the ‘free’ fields. In the higher order calculations of the resulting
perturbative expansion of the S-matrix (Scattering matrix), divergent or infinite integrals are
encountered, which involve intermediate states of arbitrarily high energies. In standard QED, these
divergencies are circumvented by redefining or ‘renormalizing’ the charge and the mass of the electron.
By the renormalization procedure, all reference to the divergencies are absorbed into a set of infinite
bare quantities. Although this procedure has made possible some of the most precise comparisons
between theory and experiment (such as the g - 2 determinations) its logical consistency and
mathematical justification remain a subject for controversies.22 Therefore, it is valuable to briefly review
how the renormalization process is related to the ZPE vacuum concept in QED.
10
The vacuum is defined as the ground state or the lowest energy state of the fields. This means
that the QED vacuum is the state where there are no photons and no electrons or positrons. However,
as we shall see in the next section, since the fields are represented by quantum mechanical operators,
they do not vanish in the vacuum state but rather fluctuate. The representation of the fields by
operators also leads to a vacuum energy (sometimes referred to as vacuum zero-point energy).
When interactions between the electromagnetic and the electron-positron field in the vacuum
are taken into account, which amounts to consider higher order contributions to the S-matrix, the
fluctuations in the energy of the fields lead to the formation of so-called virtual electron-positron pairs
(since the field operators are capable of changing the number of field quanta (particles) in a system). It
is the evaluation of contributions like these to the S-matrix that lead to the divergencies mentioned
above and prompt the need for renormalization in standard QED.
The vacuum state contains no stable particles. The vacuum in QED is believed to be the scene
of wild activity with zero-point energy and particles/anti-particles pairs constantly popping out of the
vacuum only to annihilate again immediately afterwards. This affects charged particles with oppositely
charged virtual particles and is referred to as “vacuum polarization.” Since the 1930's, for example,
theorists have proposed that virtual particles cloak the electron, in effect reducing the charge and
electromagnetic force observed at a distance.
“Vacuum polarization is, however, a relativistic effect involving electron-positron pairs, as the
hole-theoretic interpretation assumes: an electrostatic field causes a redistribution of charge in the
Dirac sea and thus polarizes the vacuum. A single charged particle, in particular, will polarize the
vacuum near it, so that its observed charge is actually smaller than its ‘bare charge.’ A proton, for
instance, will attract electrons and repel positrons of the Dirac sea, resulting in a partial screening of its
bare charge and a modification of the Coulomb potential in the hydrogen atom.”23 Even “an atom, for
instance, can be considered to be ‘dressed’ by emission and reabsorption of ‘virtual photons’ from the
vacuum.”24 This constant virtual particle flux of the ZPE is especially noticeable near the boundaries of
bigger particles, because the intense electric field gradient causes a more prodigious “decay of the
vacuum.”25
In a notable experiment designed to penetrate the virtual particle cloud surrounding the electron
(Figure 3), Koltick used a particle accelerator at energies of 58 GeV (gigaelectronvolts) without creating
other particles.26 From his data, a new value of the fine
structure constant was obtained (e2/hc = 1/128.5), while a
smaller value of 1/137 is traditionally observed for a fully
screened electron. This necessarily means that the value for a
naked electron charge is actually larger than textbooks quote
for a screened electron.
Often regarded as merely an artifact of a sophisticated
mathematical theory, some experimental verification of these
features of the vacuum has already been obtained, such as
with the Casimir pressure effect (see Figure 6). An important
reason for investigating the Casimir effect is its manifestation
Figure 3
before interactions between the electromagnetic field and the
electron/positron fields are taken into consideration. In the
language of QED, this means that the Casimir effect appears already in the zeroth order of the
perturbative expansion. In this sense the Casimir effect is the most evident feature of the vacuum. On
the experimental side, the Casimir effect has been tested very accurately.27
Some argue that there are two ways of looking at the Casimir effect:
1) The boundary plates modify an already existing QED vacuum. That is, the introduction of the
boundaries (e.g. two electrically neutral, parallel plates) modify something (a medium of vacuum zeropoint energy/vacuum fluctuations) which already existed prior to the introduction of the boundaries.
11
2) The effect is due to interactions between the microscopic constituents in the boundary plates.
That is, the boundaries introduce a source which give rise to the effect. The atomic or molecular
constituents in the boundary plates act as fluctuating sources that generate the interactions between
the constituents. The macroscopic attractive force between the two plates arises as an integrated effect
of the mutual interactions between the many microscopic constituents in these boundary plates.28
The second view is based on atoms within the boundary plates with fluctuating dipole moments
that normally give rise to van der Waals forces. Therefore, the first view, I believe, is the more modern
version, acknowledging the transformative effect of the introduction of the “Dirac sea” on modern QED
and its present view of the vacuum.29
Fluctuation-Dissipation Theorem
To conclude this introductory ZPE issues section, it is essential to review the fluctuationdissipation theorem, which is prominently featured in QED, forming the basis for the treatment of an
oscillating particle in equilibrium with the vacuum. It was originally presented in a seminal paper by
Callen et al. based on systems theory, offering applications to various systems including Brownian
motion and also electric field fluctuations in a vacuum.30 In this theorem, the vacuum is treated as a
bath coupled to a dissipative force.
“Generally speaking, if a system is coupled to a ‘bath’ that can take energy from the
system in an effectively irreversible way, then the bath must also cause fluctuations. The
fluctuations and the dissipation go hand in hand; we cannot have one without the other…the coupling
of a dipole oscillator to the electromagnetic field has a dissipative component, in the form of
radiation reaction, and a fluctuation component, in the form of zero-point (vacuum) field; given
the existence of radiation reaction, the vacuum field must also exist in order to preserve the canonical
commutation rule and all it entails.”31
The fluctuation-dissipation theorem is a generalized Nyquist relation.32 It establishes a relation
between the “impedance” in a general linear dissipative system and the fluctuations of appropriate
generalized “forces.”
The theorem itself is expressed as a single equation, essentially the same as the original
formula by Johnson from Bell Telephone Laboratory who, using kBT with equipartition, discovered the
thermal agitation “noise” of electricity,33
2 ∞
< V >=
R (ω )E(ω, T ) dω
π 0
2
∫
(11)
Here < V2 > is the root mean square (RMS) value of the spontaneously fluctuating force, R(ω) is the
generalized impedance of the system and E(ω,T) is the mean energy at temperature T of an oscillator
of natural frequency ω,
E (ω, T ) =
1
2
hω + hω
(e
hω
kT
−1
)
(12)
which is the same Planck law as Equation (9). The use of the theorem’s Equation (11) applies
exclusively to systems that have an irreversible linear dissipative portion, such as an impedance,
capable of absorbing energy when subjected to a time-periodic perturbation. This is an essential factor
to understanding the theorem’s applicability.
“The system may be said to be linear if the power dissipation is quadratic in the magnitude of
the perturbation.”34 If the condition of irreversibility is satisfied, such as with resistive heating, then the
theorem predicts that there must exist a spontaneously fluctuating force coupled to it in equilibrium.
12
This constitutes an insight into the function of the quantum vacuum in a rigorous and profound manner.
“The existence of a radiation impedance for the electromagnetic radiation from an oscillating charge is
shown to imply a fluctuating electric field in the vacuum, and application of the general theorem yields
the Planck radiation law.”35
Applying the theorem to ZPE, Callen et al. use radiation reaction as the dissipative force for
electric dipole radiation of an oscillating charge in the vacuum. Based on Equation (2), we can express
this in terms of the radiation damping constant and the change in acceleration (2nd derivative of
velocity),
Fd = 2/3(e2/c3) ∂2v/∂t2 =
Γ m ∂2v/∂t2
(13)
which is also the same equation derived by Feynman with a subtraction of retarded and advanced
fields, followed by a reduction of the particle radius Æ 0 for the radiation resistance force Fd.36 Then, the
familiar equation of motion for the accelerated charge with an applied force F and a natural frequency
ωo is
F = m ∂v/∂t + m ωo2 x + Fd
(14)
.
For an oscillating dipole and dissipative Equation (13), Callen et al. derive the real part of the
impedance from the “ratio of the in-phase component of F to v,” which can also be expressed in terms
of the radiation damping constant37
R(ω) = 2/3 (ω2e2/c3) = Γ m ω2
(15)
2
which is placed, along with Equation (12), into Equation (11). This causes < V > to yield the same
value as the energy density for isotropic radiation. Interestingly, V must then be “a randomly fluctuating
force eE on the charge” with the conclusion regarding the ZPF, “hence a randomly fluctuating electric
field E.”38
This intrinsically demonstrates the vital relationship between the vacuum fluctuation force and
an irreversible, dissipative process. The two form a complimentary relationship, analogous to Equation
(1), having great fundamental significance.
Statement of the Problem
The engineering challenge of converting or extracting zero-point energy for useful work is, at the
turn of this century, plagued by ignorance, prejudice and disbelief. The physics community does not in
general acknowledge the emerging opportunities from fundamental discoveries of zero-point energy.
Instead, there are many expositions from prominent sources explaining why the use of ZPE is
forbidden.
A scientific editorial opinion states, “Exactly how much ‘zero-point energy’ resides in the vacuum
is unknown. Some cosmologists have speculated that at the beginning of the universe, when conditions
everywhere were more like those inside a black hole, vacuum energy was high and may have even
triggered the big bang. Today the energy level should be lower. But to a few optimists, a rich supply still
awaits if only we knew how to tap into it. These maverick proponents have postulated that the zeropoint energy could explain ‘cold fusion,’ inertia, and other phenomena and might someday serve as part
of a ‘negative mass’ system for propelling spacecraft. In an interview taped for PBS’s Scientific
American Frontiers, which aired in November (1997), Harold E. Puthoff, the director of the Institute for
Advanced Studies, observed: ‘For the chauvinists in the field like ourselves, we think the 21st century
could be the zero-point-energy age.’ That conceit is not shared by the majority of physicist; some even
regard such optimism as pseudoscience that could leech funds from legitimate research. The
conventional view is that the energy in the vacuum is miniscule.”39
Dr. Robert Forward, who passed away in 2002, said, “Before I wrote the paper40 everyone
said that it was impossible to extract energy from the vacuum. After I wrote the paper, everyone
had to acknowledge that you could extract energy from the vacuum, but began to quibble about the
13
details. The spiral design won't work very efficiently... The amount of energy extracted is extremely
small... You are really getting the energy from the surface energy of the aluminum, not the vacuum...
Even if it worked perfectly, it would be no better per pound than a regular battery... Energy extraction
from the vacuum is a conservative process, you have to put as much energy into making the leaves of
aluminum as you will ever get out of the battery... etc... etc...Yes, it is very likely that the vacuum field is
a conservative one, like gravity. But, no one has proved it yet. In fact, there is an experiment mentioned
in my Mass Modification [ref. 15] paper (an antiproton in a vacuum chamber) which can check on that.
The amount of energy you can get out of my aluminum foil battery is limited to the total surface energy
of all the foils. For foils that one can think of making that are thick enough to reflect ultraviolet light, so
the Casimir attraction effect works, say 20 nm (70 atoms) thick, then the maximum amount of energy
you get out per pound of aluminum is considerably less than that of a battery. To get up to chemical
energies, you will have to accrete individual atoms using the van der Waals force, which is the Casimir
force for single atoms instead of conducting plates. My advice is to accept the fact that the vacuum field
is probably conservative, and invent the vacuum equivalent of the hydroturbine generator in a dam.”41
Professor John Barrow from Cambridge University insists that, “In the last few years a public
controversy has arisen as to whether it is possible to extract and utilise the zero-point vacuum
energy as a source of energy. A small group of physicists, led by American physicist Harold Puthoff
have claimed that we can tap into the infinite sea of zero-point fluctuations. They have so far failed to
convince others that the zero-point energy is available to us in any sense. This is a modern version of
the old quest for a perpetual motion machine: a source of potentially unlimited clean energy, at no
cost….The consensus is that things are far less spectacular. It is hard to see how we could usefully
extract zero-point energy. It defines the minimum energy that an atom could possess. If we were able
to extract some of it the atom would need to end up in an even lower energy state, which is simply not
available.”42
With convincing skeptical arguments like these from the experts, how can the extraction of ZPE
for the performance of useful work ever be considered feasible? What engineering protocol can be
theoretically developed for the extraction of ZPE if it can be reasonably considered to be
feasible? These are the central problems that are addressed by my thesis.
Purpose of the Study
This study is designed to propose a defensible feasibility argument for the extraction of ZPE
from the quantum vacuum. Part of this comprehensive feasibility study also includes an engineering
analysis of areas of research that are proving to be fruitful in the theoretical and experimental
approaches to zero-point energy extraction. A further purpose is to look at energy extraction systems,
in their various modalities, based on accepted physics and engineering principles, which may provide
theoretically fruitful areas of discovery. Lastly, a few alternate designs which are reasonable prototypes
for the extraction of zero-point energy, are also proposed.
Importance of the Study
It is unduly apparent that a study of this ubiquitous energy is overdue. The question has been
asked, “Can new technology reduce our need for oil from the Middle East?”43 More and more sectors of
our society are demanding breakthroughs in energy generation, because of the rapid depletion of oil
reserves and the environmental impact from the combustion of fossil fuels. “In 1956, the geologist M.
King Hubbert predicted that U.S. oil production would peak in the early 1970s. Almost everyone, inside
and outside the oil industry, rejected Hubbert’s analysis. The controversy raged until 1970, when the
U.S. production of crude oil started to fall. Hubbert was right. Around 1995, several analysts began
applying Hubbert’s method to world oil production, and most of them estimate that the peak year for
world oil will be between 2004 and 2008. These analyses were reported in some of the most widely
circulated sources: Nature, Science and Scientific American. None of our political leaders seem to be
paying attention. If the predictions are correct, there will be enormous effects on the world economy.”44
Figure 4 is taken from the Deffeyes book showing the Hubbert method predicting world peak oil
production and decline.
14
Figure 4
Hubbert’s Peak: it
predicted the world’s
oil production decline
It is now widely
accepted, especially in
Europe
where
I
participated in the World
Renewable
Energy
Policy
and
Strategy
Forum, Solar Energy
Expo 2002 and the Innovative Energy Technology Conference, (all in Berlin, Germany), that the world
oil production peak will probably only stretch to 2010, and that global warming is now occurring
faster than expected. Furthermore, it will take decades to reverse the damage already set in motion,
without even considering the future impact of “thermal forcing” which the future greenhouse gases will
cause from generators and automobiles already irreversibly set in motion. The Kyoto Protocol, with its
7% decrease to 1990 levels of emissions, is a small step in the right direction but it does not address
the magnitude of the problem, nor attempt to reverse it. “Stabilizing atmospheric CO2 concentrations at
safe levels will require a 60 – 80 per cent cut in carbon emissions from current levels, according to the
best estimates of scientists.”45 Therefore, renewable energy sources like solar and wind power have
seen a dramatic increase in sales every single year for the past ten years as more and more people
see the future shock looming on the horizon. Solar photovoltaic panels, however, still have to reach the
wholesale level in their cost of electricity that wind turbines have already achieved.
Another emerging problem that seems to have been unanticipated by the environmental groups
is that too much proliferation of one type of machinery, such as windmills, can be objectionable as well.
Recently, the Alliance to Protect Nantucket Sound filed suit against the U.S. Army Corps of Engineers
to stop construction of a 197-foot tower being built to collect wind data for the development of a wind
farm 5 miles off the coast of Massachusetts. Apparently, the wealthy residents are concerned that the
view of Nantucket Sound will be spoiled by the large machines in the bay.46 Therefore, it is likely that
only a compact, distributed, free energy generator will be acceptable to the public in the future.
Considering payback-on-investment, if it possessed a twenty-five year lifespan or more, while requiring
minimum maintenance, then it will probably please most of the people, most of the time. The
development of a ZPE generator theoretically would actually satisfy these criteria.
Dr. Steven Greer of the Disclosure Project has stated, “classified above top-secret projects
possess fully operational anti-gravity propulsion devices and new energy generation systems,
that, if declassified and put to peaceful uses, would empower a new human civilization without want,
poverty or environmental damage.”47
However, since the declassification of black project,
compartmentalized exotic energy technologies is not readily forthcoming, civilian physics research is
being forced to reinvent fueless energy sources such as zero-point energy extraction.
Regarding the existing conundrum of interplanetary travel, with our present lack of appropriate
propulsion technology and cosmic ray bombardment protection, Arthur C. Clarke has predicted, that in
3001 the “inertialess drive” will most likely be put to use like a controllable gravity field, thanks to the
landmark paper by Haisch et al.48 “…if HR&P’s theory can be proved, it opens up the prospect—
however remote—of antigravity ‘space drives,’ and the even more fantastic possibility of controlling
inertia.”49
15
Rationale of the Study
The hypothesis of the study is centered on the accepted physical basis for zero-point energy, its
unsurpassed energy density, and the known physical manifestations of zero-point energy, proven by
experimental observation. Conversion of energy is a well-known science which can, in theory, be
applied to zero-point energy.
The scope of the study encompasses the known areas of physical discipline: mechanical,
thermal, fluidic, and electromagnetic. Within these disciplines, the scope also extends from the
macroscopic beyond the microscopic to the atomic. This systems science approach, which is fully
discussed and analyzed in Chapter 4, includes categories such as:
1. Electromagnetic conversion of zero-point energy radiation
2. Fluidic entrainment of zero-point energy flow through a gradient
3. Mechanical conversion of zero-point energy force or pressure
4. Thermodynamic conversion of zero-point energy.
Definition of Terms
Following are terms that are used throughout the study:
1.
Bremsstrahlung: Radiation caused by the deceleration of an electron. Its energy is converted into
light. For heavier particles the retardations are never so great as to make the radiation
important.50
2.
Dirac Sea: The physical vacuum in which particles are trapped in negative energy states until
enough energy is present locally to release them.
3.
Energy: The capacity for doing work. Equal to power exerted over time (e.g. kilowatt-hours). It can
exist in linear or rotational form and is quantized in the ultimate part. It may be conserved or not
conserved, depending upon the system considered. Mostly all terrestrial manifestations can be
traced to solar origin, except for zero-point energy.
4.
Lamb Shift: A shift (increase) in the energy levels of an atom, regarded as a Stark effect, due to
the presence of the zero-point field. Its explanation marked the beginning of modern quantum
electrodynamics.
5.
Parton: The fundamental theoretical limit of particle size thought to exist in the vacuum, related to
the Planck length (10-35 meter) and the Planck mass (22 micrograms), where quantum effects
dominate spacetime. Much smaller than subatomic particles, it is sometimes referred to as the
charged point particles within the vacuum that participate in the ZPE Zitterbewegung.
6.
Planck’s Constant: The fundamental basis of quantum mechanics which provides the measure of
a quantum (h = 6.6 x 10-34 joule-second), it is also the ratio of the energy to the frequency of a
photon.
7.
Quantum Electrodynamics: The quantum theory of light as electromagnetic radiation, in wave and
particle form, as it interacts with matter. Abbreviated “QED.”
8.
Quantum Vacuum: A characterization of empty space by which physical particles are
unmanifested or stored in negative energy states. Also called the “physical vacuum.”
9.
Uncertainty Principle: The rule or law that limits the precision of a pair of physical measurements
in complimentary fashion, e.g. the position and momentum, or the energy and time, forming the
basis for zero-point energy.
10.
Virtual Particles: Physically real particles emerging from the quantum vacuum for a short time
determined by the uncertainty principle. This can be a photon or other particle in an intermediate
state which, in quantum mechanics (Heisenberg notation) appears in matrix elements connecting
16
initial and final states. Energy is not conserved in the transition to or from the intermediate state.
Also known as a virtual quantum.
11.
Zero-point energy: The non-thermal, ubiquitous kinetic energy (averaging ½hf) that is manifested
even at zero degrees Kelvin, abbreviated as “ZPE.” Also called vacuum fluctuations, zero-point
vibration, residual energy, quantum oscillations, the vacuum electromagnetic field, virtual particle
flux, and recently, dark energy.
12.
Zitterbewegung: An oscillatory motion of an electron, exhibited mainly when it penetrates a
voltage potential, with frequency greater than 1021 Hertz. It can be associated with pair production
(electron-positron) when the energy of the potential exceeds 2mc2 (m = electron mass). Also
generalized to represent the rapid oscillations associated with zero-point energy.
Overview of the Study
In all of the areas of investigation, so far no known extractions of zero-point energy for useful
work have been achieved, though it can be argued that incidental ZPE extraction has manifested itself
macroscopically. By exploring the main physical principles underlying the science of zero-point energy,
certain modalities for energy conversion achieve prominence while others are regarded as less
practical. Applying physics and engineering analysis, a scientific research feasibility study of ZPE
extraction, referenced by rigorous physics theory and experiment is generated.
With a comprehensive survey of conversion modalities, new alternate, efficient methods for ZPE
extraction are presented and analyzed. Comparing the specific characteristics of zero-point energy with
the known methods of energy conversion, the common denominators should offer the most promising
feasibility for conversion of zero-point energy into useful work. The advances in nanotechnology are
also examined, especially where ZPE effects are already identified as interfering with mechanical and
electronic behavior of nanodevices.
17
CHAPTER 2 - Review of Related Literature
Historical Perspectives
Reviewing the literature for zero-point energy necessarily starts with the historical developments
of its discovery. In 1912, Max Planck published the first journal article to describe the discontinuous
emission of radiation, based on the discrete quanta of energy.51 In this paper, Planck’s now-famous
“blackbody” radiation equation contains the residual energy factor, one half of hf, as an additional term
(½hf), dependent on the frequency f, which is always greater than zero (where h = Planck’s constant). It
is therefore widely agreed that “Planck’s equation marked the birth of the concept of zero-point
energy.”52 This mysterious factor was understood to signify the average oscillator energy available to
each field mode even when the temperature reaches absolute zero. In the meantime, Einstein had
published his “fluctuation formula” which describes the energy fluctuations of thermal radiation.53
Today, “the particle term in the Einstein fluctuation formula may be regarded as a consequence of zeropoint field energy.”54
During the early years of its discovery, Einstein55,56 and Dirac57,58 saw the value of zero-point
energy and promoted its fundamental importance. The 1913 paper by Einstein computed the specific
heat of molecular hydrogen, including zero-point energy, which agreed very well with experiment.
Debye also made calculations including zero-point energy (ZPE) and showed its effect on Roentgen ray
(X-ray) diffraction.59
Throughout the next few decades, zero-point energy became intrinsically important to quantum
mechanics with the birth of the uncertainty principle. “In 1927, Heisenberg, on the basis of the Einsteinde Broglie relations, showed that it is impossible to have a simultaneous knowledge of the [position]
coordinate x and its conjugate momentum p to an arbitrary degree of accuracy, their uncertainties being
given by the relation Δx Δp > h / 4π.”60 This expression of Equation (1) is not the standard form that
Heisenberg used for the uncertainty principle, however. He invented a character h called “h-bar,” which
equals h/2π (also introduced in Chapter 1). If this shortcut notation is used for the uncertainty principle,
it takes the form Δx Δp > h / 2 or ΔE Δt > h / 2, which is a more familiar equation to physicists and found
in most quantum mechanics texts.
By 1935, the application of harmonic oscillator models with various boundary conditions became
a primary approach to quantum particle physics and atomic physics.61 Quantum mechanics also
evolved into “wave mechanics” and “matrix mechanics” which are not central to this study. However,
with the evolution of matrix mechanics came an intriguing application of matrix “operators” and
“commutation relations” of x and p that today are well known in quantum mechanics. With these new
tools, the “quantization of the harmonic oscillator” is all that is required to reveal the existence of the
zero-point ground state energy.62
“This residual energy is known as the zero-point energy, and is a direct consequence of the
uncertainty principle. Basically, it is impossible to completely stop the motion of the oscillator, since if
the motion were zero, the uncertainty in position Δx would be zero, resulting in an infinitely large
uncertainty in momentum (since Δp = h / 2Δx). The zero-point energy represents a sharing of the
uncertainty in position and the uncertainty in momentum. The energy associated with the uncertainty in
momentum gives the zero-point energy.”63
Another important ingredient in the development of the understanding of zero-point energy
came from the Compton effect. “Compelling confirmation of the concept of the photon as a
concentrated bundle of energy was provided in 1923 by A. H. Compton who earned a Nobel prize for
this work in 1927.”64 Compton scattering, as it is now known, can only be understood using the
energy-frequency relation E = hf that was proposed previously by Einstein to explain the photoelectric
effect in terms of Planck’s constant, h.65
18
Ruminations about the zero-point vacuum field (ZPF), in conjunction with Einstein’s famous
equation E = mc2 and the limitations of the uncertainty principle, suggested that photons may also be
created and destroyed “out of nothing.” Such photons have been called “virtual” and are prohibited by
classical laws of physics. “But in quantum mechanics the uncertainty principle allows energy
conservation to be violated for a short time interval Δt = h / 2ΔE. As long as the energy is
conserved after this time, we can regard the virtual particle exchange as a small fluctuation of energy
that is entirely consistent with quantum mechanics.”66 Such virtual particle exchanges later became an
integral part of an advanced theory called quantum electrodynamics (QED) where “Feynmann
diagrams,” developed by Nobel-prize winner Richard Feynmann to describe particle collisions, often
show the virtual photon exchange between the paths of two nearby particles.67 Figure 5 shows a
sample of the Compton scattering of a virtual photon as it contributes to the radiated energy effect of
bremsstrahlung (see Definition of Terms on page 15).68
Casimir Predicts a Measurable ZPE Effect
In 1948, it was predicted that virtual particle appearances should exert a force that is
measurable.69 Casimir not only predicted the presence of such a force but also explained why van der
Waals forces dropped off unexpectedly at long range separation between atoms. The Casimir effect
was first verified experimentally using a variety of conductive plates by Sparnaay.70
Figure 5 – A virtual
photon hits a particle
causing deflection
(Compton scattering)
which QED also
analyzes as (a) and (b)
There was still an interest for an improved test of the Casimir force using conductive plates as
modeled in Casimir's paper to better accuracy than Sparnaay. In 1997, Dr. Lamoreaux, from Los
Alamos Labs, performed the experiment with less than one micrometer (micron) spacing between goldplated parallel plates attached to a torsion pendulum.71 In retrospect, he found it to one of the most
intellectually satisfying experiments that he ever performed since the results matched the theory so
closely (within 5%). This event also elevated zero-point energy fluctuations to a higher level of public
interest. Even the New York Times covered the event.72
The Casimir Effect has been posited as a force produced solely by activity in the empty vacuum
(see Figure 6). The Casimir force is also very powerful at small distances. Besides being independent
of temperature, it is inversely proportional to the fourth power of the distance between the plates at
larger distances and inversely proportional to the third power of the distance between the plates at
short distances.73 (Its frequency dependence is a third
power.)
Figure 6
Lamoreaux's results come as no surprise to
anyone familiar with quantum electrodynamics, but they
serve as a material confirmation of a bazaar theoretical
prediction: that QED predicts the all-pervading vacuum
continuously spawns particles and waves that
spontaneously pop in and out of existence. Their time of
existence is strictly limited by the uncertainty principle but
they create some havoc while they bounce around during
their brief lifespan. The churning quantum foam is
believed to extend throughout the universe even filling the
empty space within the atoms in human bodies. Physicists theorize that on an infinitesimally small
scale, far, far smaller than the diameter of atomic nucleus, quantum fluctuations produce a foam of
19
erupting and collapsing, virtual particles, visualized as a topographic distortion of the fabric of space
time (Figure 7).
Ground State of Hydrogen is Sustained by ZPE
Looking at the electron in a set ground-state orbit, it consists of a bound state with a central
Coulomb potential that has been treated successfully in physics with the harmonic oscillator model.
However, the anomalous repulsive force balancing the attractive Coulomb potential remained a mystery
until Puthoff published a ZPE-based description of
the hydrogen ground state.74 This derivation caused
a stir among physicists because of the extent of
influence that was now afforded to vacuum
fluctuations. It appears from Puthoff’s work that the
ZPE shield of virtual particles surrounding the
electron may be the repulsive force. Taking a
simplistic argument for the rate at which the atom
absorbs energy from the vacuum field and equating
Figure 7 – Quantum foam
it to the radiated loss of energy from accelerated
charges, the Bohr quantization condition for the
ground state of a one-electon atom like hydrogen is obtained. “We now know that the vacuum field is in
fact formally necessary for the stability of atoms in quantum theory.”75
Lamb Shift Caused by ZPE
Another historically valid test in the
verification of ZPE has been what has been
called the “Lamb shift.” Measured by Dr. Willis
Lamb in the 1940's, it actually showed the
effect of zero point fluctuations on certain
electron levels of the hydrogen atom, causing a
fine splitting of the levels on the order of 1000
MHz.76 Physicist Margaret Hawton describes
the Lamb shift as “a kind of one atom Casimir
Effect” and predicts that the vacuum
fluctuations of ZPE need only occur in the
vicinity of atoms or atomic particles.77 This
seems to agree with the discussion about
Koltick in Chapter 1, illustrated in Figure 3.
Today, “the majority of physicists
attribute spontaneous emission and the Lamb
shift entirely to vacuum fluctuations.”78 This
may lead scientists to believe that it can no
longer be called "spontaneous emission" but
instead should properly be labeled forced or
"stimulated emission" much like laser light,
even though there is a random quality to it.
However, it has been found that radiation
reaction (the reaction of the electron to its own
field) together with the vacuum fluctuations
contribute equally to the phenomena of
spontaneous emission.79
Figure 8
20
Experimental ZPE
The first journal publication to propose a Casimir machine for "the extracting of electrical energy
from the vacuum by cohesion of charge foliated conductors" is summarized here.80 Dr. Forward
describes this "parking ramp" style corkscrew or spring as a ZPE battery that will tap electrical energy
from the vacuum and allow charge to be stored. The spring tends to be compressed from the Casimir
force but the like charge from the electrons stored will cause a repulsion force to balance the spring
separation distance. It tends to compress upon dissipation and usage but expand physically with
charge storage. He suggests using micro-fabricated sandwiches of ultrafine metal dielectric layers.
Forward also points out that ZPE seems to have a definite potential as an energy source.
Another interesting experiment is the "Casimir Effect at Macroscopic Distances" which proposes
observing the Casimir force at a distance of a few centimeters using confocal optical resonators within
the sensitivity of laboratory instruments.81 This experiment makes the microscopic Casimir effect
observable and greatly enhanced.
In general, many of the experimental journal articles refer to vacuum effects on a cavity that is
created with two or more surfaces. Cavity QED is a science unto itself. “Small cavities suppress atomic
transitions; slightly larger ones, however, can enhance them. When the size of the cavity surrounding
an excited atom is increased to the point where it matches the wavelength of the photon that the atom
would naturally emit, vacuum-field fluctuations at that wavelength flood the cavity and become stronger
than they would be in free space.”82 It is also possible to perform the opposite feat. “Pressing zero-point
energy out of a spatial region can be used to temporarily increase the Casimir force.”83 The materials
used for the cavity walls are also important. It is well-known that the attractive Casimir force is obtained
from highly reflective surfaces. However, “…a repulsive Casimir force may be obtained by considering
a cavity built with a dielectric and a magnetic plate. The product r of the two reflection amplitudes is
indeed negative in this case, so that the force is repulsive.”84 For parallel plates in general, a
“magnetic field inhibits the Casimir effect.”85
An example of an idealized system with two parallel semiconducting plates separated by an
variable gap that utilizes several concepts referred to above is Dr. Pinto’s “optically controlled vacuum
energy transducer.”86 By optically pumping the cavity with a microlaser as the gap spacing is varied,
“the total work done by the Casimir force along a closed path that includes appropriate transformations
does not vanish…In the event of no other alternative explanations, one should conclude that major
technological advances in the area of endless, by-product free-energy production could be achieved.”87
More analysis on this revolutionary invention will be presented in Chapter 4.
ZPE Patent Review
For any researcher reviewing the literature for an invention design such as energy transducers,
it is well-known in the art that it is vital to perform a patent search. In 1987, Werner and Sven from
Germany patented a “Device or method for generating a varying Casimir-analogous force and liberating
usable energy” with patent #DE3541084. It subjects two plates in close proximity to a fluctuation which
they believe will liberate energy from the zero-point field.
In 1996, Jarck Uwe from France patented a “Zero-point energy power plant” with PCT patent
#WO9628882. It suggests that a coil and magnet will be moved by ZPE which then will flow through a
hollow body generating induction through an energy whirlpool. It is not clear how such a macroscopic
apparatus could resonate or respond to ZPE effectively.
On Dec. 31, 1996 the conversion of ZPE was patented for the first time in the United States with
US patent #5,590,031. The inventor, Dr. Frank Mead, Director of the Air Force Research Laboratory,
designed receivers to be spherical collectors of zero point radiation (see Figure 9). One of the
interesting considerations was to design it for the range of extremely high frequency that ZPE offers,
which by some estimates, corresponds to the Planck frequency of 1043 Hz. We do not have any
apparatus to amplify or even oscillate at that frequency currently. For example, gigahertz radar is only
1010 Hz or so. Visible light is about 1014 Hertz and gamma rays reach into the 20th power, where the
21
wavelength is smaller than the size of an atom. However, that's still a long way off from the 40th power.
The essential innovation of the Mead patent is the “beat frequency” generation circuitry, which creates
a lower frequency output signal from the ZPE input.
Another patent that utilizes a noticeable ZPE effect is the AT&T “Negative Transconductance
Device” by inventor, Federico Capasso (US #4,704,622). It is a resonant tunneling device with a onedimensional quantum well or wire. The important energy consideration involves the additional zeropoint energy which is available to the electrons in the extra dimensional quantized band, allowing them
to tunnel through the barrier. This solid state, multi-layer, field effect transistor demonstrates that
without ZPE, no tunneling would be possible. It is supported by the virtual photon tunnel
effect.88
Grigg's Hydrosonic Pump is another patent (U.S. #5,188,090), whose water glows blue when in
cavitation mode, that consistently has been measuring an
over-unity performance of excess heat energy output. It
appears to be a dynamic Casimir effect that contributes to
sonoluminescence.89
Joseph
Yater
patented
his
“Reversible
Thermoelectric Converter with Power Conversion of Energy
Fluctuations” (#4,004,210) in 1977 and also spent years
defending it in the literature. In 1974, he published “Power
conversion of energy fluctuations.”90 In 1979, he published
an article on the “Relation of the second law of
thermodynamics to the power conversion of energy
fluctuations”91 and also a rebuttal to comments on his first
article.92 It is important that he worked so hard to support
such a radical idea, since it appears that energy is being
brought from a lower temperature reservoir to a higher one,
which normally violates the 2nd law. The basic concept is a
simple rectification of thermal noise, which also can be found
in the Charles Brown patent (#3,890,161) of 1975, “Diode
array for rectifying thermal electrical noise.”
Figure 9
Many companies are now very interested in such processes for powering nanomachines. While
researching this ZPE thesis, I attended the AAAS workshop by IBM on nanotechnology in 2000, where
it was learned that R. D. Astumian proposed in 1997 to rectify thermal noise (as if this was a new
idea).93 This apparently has provoked IBM to begin a “nanorectifier” development program.
Details of some of these and other inventions are analyzed in Chapter 4.
ZPE and Sonoluminescence
Does sonoluminescence (SL) tap ZPE? This question is based upon the experimental results of
ultrasound cavitation in various fluids which emit light and extreme heat from bubbles 100 microns in
diameter which implode violently creating temperatures of 5,500 degrees Celsius. Scientists at UCLA
have recently measured the length of time that sonoluminescence flashes persist. Barber discovered
that they only exist for 50 picoseconds (ps) or shorter, which is too brief for the light to be produced by
some atomic process. Atomic processes, in comparison, emit light for at least several tenths of a
nanosecond (ns). “To the best of our resolution, which has only established upper bounds, the light
flash is less than 50 ps in duration and it occurs within 0.5 ns of the minimum bubble radius. The SL
flashwidth is thus 100 times shorter than the shortest (visible) lifetime of an excited state of a hydrogen
atom.”94
Critical to the understanding of the nature of this light spectrum however, is what other
mechanism than atomic transitions can explain SL. Dr. Claudia Eberlein in her pioneering paper
"Sonoluminescence and QED" describes her conclusion that only the ZPE spectrum matches the light
22
emission spectrum of sonoluminescence, and could react as quickly as SL.95 She thus concludes that
SL must therefore be a ZPE phenomena. It is also acknowledged that “Schwinger proposed a physical
mechanism for sonoluminescence in terms of photon production due to changes in the properties of the
quantum-electrodynamic (QED) vacuum arising from a collapsing dielectric bubble.”96
Gravity and Inertia Related to ZPE
Another dimension of ZPE is found in the work of Dr. Harold Puthoff, who has found that gravity
is a zero-point-fluctuation force, in a prestigious Physical Review article that has been largely
uncontested.97 He points out that the late Russian physicist, Dr. Sakharov regarded gravitation as not a
fundamental interaction at all, but an induced effect that's brought about by changes in the vacuum
when matter is present. The interesting part about this is that the mass is shown to correspond to the
kinetic energy of the zero-point-induced internal particle jittering, while the force of gravity is comprised
of the long ZPE wavelengths. This is in the same category as the low frequency, long range forces that
are now associated with Van der Waal's forces.
Referring to the inertia relationship to zero-point energy, Haisch et al. find that first of all, that
inertia is directly related to the Lorentz Force which is used to describe Faraday's Law.98 As a result of
their work, the Lorentz Force now has theoretically been shown to be directly responsible for an
electromagnetic resistance arising from a distortion of the zero-point field in an accelerated
frame. They also explain how the magnetic component of the Lorentz force arises in ZPE, its matter
interactions, and also a derivation of Newton’s law, F = ma. From quantum electrodynamics, Newton’s
law appears to be related to the known distortion of the zero point spectrum in an accelerated reference
frame.
Haisch et al. present an understanding as to why force and acceleration should be related, or
even for that matter, what is mass.99 Previously misunderstood, mass (gravitational or inertial) is
apparently more electromagnetic than mechanical in nature. The resistance to acceleration defines the
inertia of matter but interacts with the vacuum as an electromagnetic resistance. To summarize the
inertia effect, it is connected to a distortion at high frequencies of the zero-point field. Whereas, the
gravitational force has been shown to be a low frequency interaction with the zero point field.
Recently, Alexander Feigel has proposed that the momentum of the virtual photons can
depend upon the direction in which they are traveling, especially if they are in the presence of
electric or magnetic fields. His theory and experiment offers a possible explanation for the
accelerated expansion of distant galaxies.100
Heat from ZPE
In what may seem to appear as a major contradiction, it has been proposed that, in principle,
basic thermodynamics allows for the extraction of heat energy from the zero-point field via the Casimir
force. “However, the contradiction becomes resolved upon recognizing that two different types of
thermodynamic operations are being discussed.”101 Normal thermodynamically reversible heat
generation process is classically limited to temperatures above absolute zero (T > 0 K). “For heat to be
generated at T = 0 K, an irreversible thermodynamic operation needs to occur, such as by taking the
systems out of mechanical equilibrium.”102 Examples are given of theoretical systems with two opposite
charges or two dipoles in a perfectly reflecting box being forced closer and farther apart. Adiabatic
expansion and irreversible adiabatic free contraction curves are identified on a graph of force versus
distance with reversible heating and cooling curves connecting both endpoints. Though a practical
method of energy or heat extraction is not addressed in the article, the basis for designing one is given
a physical foundation.
A summary of all three ZPE effects introduced above (heat, inertia, and gravity) can be found in
the most recent Puthoff et al. publication entitled, “Engineering the Zero-Point Field and Polarizable
Vacuum for Interstellar Flight.”103 In it they state, “One version of this concept involves the projected
possibility that empty space itself (the quantum vacuum, or space-time metric) might be manipulated so
as to provide energy/thrust for future space vehicles. Although far-reaching, such a proposal is solidly
23
grounded in modern theory that describes the vacuum as a polarizable medium that sustains energetic
quantum fluctuations.”104 A similar article proposes that “monopolar particles could also be accelerated
by the ZPF, but in a much more effective manner than polarizable particles.”105 Furthermore, “…the
mechanism should eventually provide a means to transfer energy…from the vacuum electromagnetic
ZPF into a suitable experimental apparatus.”106 With such endorsements for the use of ZPE, the value
of this present study seems to be validated and may be projected to be scientifically fruitful.
Summary
To summarize the scientific literature review, the experimental evidence for the existence of
ZPE include the following:
1) Anomalous magnetic moment of the electron107
2) Casimir effect108
3) Diamagnetism109
4) Einstein’s fluctuation formula110
5) Gravity111
6) Ground state of the hydrogen atom112
7) Inertia113
8) Lamb shift114
9) Liquid Helium to T = 0 K115
10) Planck’s blackbody radiation equation116
11) Quantum noise117
12) Sonoluminescence118
13) Spontaneous emission119
14) Uncertainty principle120
15) Van der Waals forces121
The apparent discrepancy in the understanding of the concepts behind ZPE comes from the fact
that ZPE evolves from classical electrodynamics theory and from quantum mechanics. For example,
Dr. Frank Mead (US Patent #5,590,031) calls it "zero point electromagnetic radiation energy" following
the tradition of Timothy Boyer who simply added a randomizing parameter to classical ZPE theory thus
inventing “stochastic electrodynamics” (SED).122 Lamoreaux, on the other hand, refers to it as "a flux of
virtual particles", because the particles that react and create some of this energy are popping out of the
vacuum and going back in.123 The New York Times simply calls it "quantum foam." But the important
part about it is from Dr. Robert Forward, "the quantum mechanical zero point oscillations are
real."124
24
CHAPTER 3 - Methodology
In this chapter, the methods used in this research feasibility study will be reviewed, including the
approach, the data gathering method, the database selected for analysis, the analysis of the data, the
validity of the data, the uniqueness (originality) and limitations of the method, along with a brief
summary.
Approach
The principal argument for the feasibility study of zero-point energy extraction is that it provides
a systematic way of evaluating the fundamental properties of this phenomena of nature. Secondly,
research into the properties of ZPE offer an opportunity for innovative application of basic principles of
energy conversion. These basic transduction methods fall into the disciplines of mechanical, fluidic,
thermal, and electrical systems.125 It is well-known that these engineering systems find application in all
areas of energy generation in our society. Therefore, it is reasonable that this study utilize a systems
approach to zero-point energy conversion while taking into consideration the latest quantum
electrodynamic findings regarding ZPE.
There are several important lessons that can be conveyed by a feasibility study of ZPE
extraction.
1) It permits a grounding of observations and concepts about ZPE in a scientific setting with an
emphasis toward engineering practicability.
2) It furnishes information from a number of sources and over a wide range of disciplines,
which is important for a maximum potential of success.
3) It can provide the dimension of history to the study of ZPE thereby enabling the investigator
to examine continuity and any change in patterns over time.
4) It encourages and facilitates, in practice, experimental assessment, theoretical innovation
and even fruitful generalizations.
5) It can offer the best possible avenues, which are available for further research and
development, for the highest probability of success.
A feasibility study enables an investigation to take place into every detail of the phenomena being
researched. The feasibility study is an effective vehicle for providing an overview of the breadth and
depth of the subject at hand, while providing the reader an opportunity to probe for internal consistency.
What is a Feasibility Study?
A feasibility study is a complete examination of the practicability of a specific invention, project,
phenomena, or process. It strives to provide the requisite details necessary to support its conclusion
concerning the possibility or impossibility of accomplishing the goal of the research study. As such, it
takes an unbiased viewpoint toward the subject matter and reflects a balanced presentation of the facts
that are currently available in the scientific literature.
Feasibility studies are the hallmark of engineering progress, often saving investors millions of
dollars, while providing a superior substitute for risk assessment. Therefore, such studies are required
before any consideration is made of the investment potential of an invention, project, process, or
phenomena by venture capitalists. Feasibility studies thus provide all of the possible engineering details
that can be presented beforehand so that the construction stage can proceed smoothly and with a
prerequisite degree of certitude as to the outcome.
Feasibility studies can also provide a wealth of information just with the literature survey that is
an integral part of the research. Along with the survey, an expert engineering and physics assessment
is usually provided regarding the findings reported in the literature and how they directly relate to the
capability of the process, phenomena, project, or invention to be put into effect.
25
As such, a feasibility study offers the best possible original research of the potential for
successful utilization, with a thick descriptive style so necessary for an accurate and honest
judgment.126
“A good feasibility study will contain clear supporting evidence for its recommendations. It’s best
to supply a mix of numerical data with qualitative, experience-based documentation (where
appropriate). The report should also indicate a broad outline of how to undertake any recommended
development work. This will usually involve preparing an initial, high-level project plan that estimates
the required project scope and resources and identifies major milestones. An outline plan makes
everyone focus more clearly on the important implementation issues and generate some momentum for
any subsequent work. This is especially true if feasibility teams suspect that the development itself will
become their baby. A sound, thorough feasibility study will also ease any subsequent development
tasks that gain approval. The feasibility study will have identified major areas of risk and outlined
approaches to dealing with these risks. Recognising the nature of feasibility projects encourages the
successful implementation of the best ideas in an organisation and provides project managers with
some novel challenges.”127
Data Gathering Method
The method used in this feasibility study is the same that is used in pure as well as applied
research. Through a review of the scientific literature, certain approaches to the conversion of zeropoint energy into useful work demonstrate more promise and engineering feasibility than others.
Combining the evaluation with the known theories and experimental discoveries of zero-point energy
and the author’s professional engineering knowledge of electromechanical fabrication, a detailed
recommendation and assessment for the most promising and suitable development is then made. This
procedure follows the standard method used in most feasibility studies.128,129,130
Database Selected for Analysis
The database for this study consists of mostly peer-reviewed physics journals, engineering
journals, science magazines, patent literature, textbooks, which are authored by physicists and
engineers.
Analysis of Data
The analysis of the data is found in Chapter 4, where the findings are explored. The most
promising possibilities, from an engineering standpoint, are the zero-point energy conversion concepts
that are past the research stage or the proof-of-principle stage and into the developmental arena. Using
the scientific method, a thorough examination of the data is presented, with physics and engineering
criteria, to determine the feasibility of zero-point energy extraction.
Validity of Data
The data used in this study can be presumed to be valid beyond a reasonable doubt. Ninety
years ago, when zero-point energy was first discovered, the validity of the data may have been
questioned. However, after so much experimental agreement with theory has followed in the physics
literature, it can be said that the data has stood the test of time. Furthermore, in the past decade, there
has been a dramatic increase in the number of journal publications on the subject of zero-point energy,
demonstrating the timeliness and essential value of this study. Excluding any anomalous findings that
have not been replicated or verified by other scientists, it can be presumed that the data presented in
this feasibility study represents the highest quality that the scientific community can offer.
Uniqueness and Limitations of the Method
The method applied in this study, though it appears to be universal in its approach, is being
applied for the first time to determine the utility of zero-point energy extraction. Only through
experimental verification can the method be validated. However, many intermediate steps required for
utilization have already been validated by experiment, as mentioned in the above sections.
26
As with any study of this nature, certain limitations are inherent in the method. The feasibility
study draws from a large database and involves a great number of variables, which is, in itself, a
limitation. The nature of ZPE is also a limitation because it is so unusual and foreign to most scientists,
while many standard testing methods used for other fields and forces fail to reveal its presence.
These variables and limitations have been minimized to every extent possible.
Summary
The method used in this feasibility study is the application of the basic principles of energy
conversion in the mechanical, fluidic, thermal, and electromagnetic systems to zero-point energy
research. It is a systems approach that has a fundamental basis in the scientific method. By reviewing
journal articles and textbooks in the physics and engineering field of zero-point energy, certain data has
been accumulated. The analysis of the data is conducted in a critical manner with an approximate
rating system in order to evaluate the practical applications of both theory and experiment, and the
likelihood of success for energy conversion. It is believed that this is the first time such an
approach has been used and applied to the field of zero-point energy conversion. As such, new
and exciting conclusions are bound to emerge.
27
CHAPTER 4 - Analysis
Introduction to Vacuum Engineering
The emerging discipline of vacuum engineering encompasses the present investigation into
energy conversion modalities that offer optimum feasibility. It is believed by only a minority of physicists
that the vacuum can be engineered to properly facilitate the transduction of energy to useful work. In
this chapter, two intriguing energy converters (Electromagnetic and Casimir) are examined and
analyzed according to the methodology outlined in Chapter 3. Then, several ZPE techniques for the
vacuum engineer’s toolkit are examined, such as focusing vacuum fluctuations, spatial squeezing, etc.
The scope of this feasibility study is detailed in Chapter 1 and will include zero-point energy
conversion methodologies in the areas of electromagnetism, fluid mechanics, thermodynamics,
mechanical physics, and some quantum theories.
Vacuum engineering considerations often exhibit a particular bias toward wave or particle. It is
difficult or perhaps impossible to design a zero-point energy converter that will utilize both wave and
particle aspects of the quantum vacuum, since the size of the transducer determines which will
dominate.
Electromagnetic Zero-Point Energy Converter
Treating the quantum vacuum initially as an all-pervading electromagnetic wave with a high
bandwidth is a classical physics approach. Among various examples, the most intriguing is a U.S.
patent (#5,590,031) proposing microscopic antennae for collecting and amplifying zero-point
electromagnetic energy. Introduced in Figure 9, it is a US Air Force invention by Mead et al. that
offers sufficient scientific rigor and intrigue to warrant further analysis. The patent’s spherical
resonators are small scatterers of the zero-point vacuum flux and capitalize on the electromagnetic
wave nature of the ZPF. Utilizing this design to start the inquiry at least into the microscopic and
nanotechnology realm, it is helpful to review the key design parameters in the Mead patent,
•
the energy density increases with frequency (col. 7, line 63),
•
the spheres are preferably microscopic in size (col. 8, line 3),
•
a volume of close proximity spheres enhances output (col. 8, line 20),
•
resonant “RHO values” which correspond to propagation values are sought for which
coefficients an or bn is infinity (col. 6, line 40),
•
spherical structures are of different size so that the secondary fields will be a lower
frequency than the incident radiation (col. 3, line 7),
•
the converter circuitry may also include a transformer for voltage optimization and possibly a
rectifier to convert the energy into a direct current (col. 3, line 30),
•
the system also includes an antenna which receives the beat frequency (col. 7, line 35).
It is noted in the patent that “zero point radiation is homogeneous and isotropic as well as
ubiquitous. In addition, since zero point radiation is also invariant with respect to Lorentz
transformation, the zero point radiation spectrum has the characteristic that the intensity of the radiation
at any frequency is proportional to the cube of that frequency” (col. 1, line 30). This sets the stage for
an optimum design of the highest frequency collector possible that the inventors believe will work
anywhere in the universe.
Another area of interest upon review is the opinion of the inventors that, “At resonance,
electromagnetically induced material deformations of the receiving structures produce secondary fields
of electromagnetic energy therefrom which may have evanescent energy densities several times that of
28
the incident radiation” (col. 2, line 65). However, this does not seem to be a physically justifiable
statement, nor is it defended anywhere else in the patent. Furthermore, the discussion diverges and
instead proceeds toward the formation of “beat frequencies” which are produced through interference
resulting in the sum and difference of two similar frequencies. It is noted that the subtraction of the
frequencies from two receivers of slightly different size is of primary importance to the invention claimed
(col. 3, line 7).
The engineering considerations in the patent include the statement that “packing a volume with
such spheres in close proximity could enhance the output of energy” (col. 8, line 20). The enhancement
referred to here is understood to mean the multiplied effect from having several interference sources for
the beat frequency production and amplification. Upon researching this aspect of the invention, it is
found however, that scattering by a collection of scatterers can actually reduce the output of energy,
especially if the spheres are randomly distributed. In that case, an incoherent superposition of individual
contributions will have destructive instead of constructive interference. A large regular array of
scatterers, even if transparent, tends to absorb rather than scatter, such as a simple cubic array of
scattering centers in a rock salt or quartz crystal.131
This crucial feature of the patent involving the receiver’s output involves a method for analyzing
electromagnetic or Mie scattering from dielectric spheres132 (col. 4, line 60). The patent relies upon a
report detailing the calculations by Cox (which has been obtained from the inventor) of two infinite
series equations for the electric and magnetic components of the spherical reflection of incident
electromagnetic waves.133 The report, summarized in the patent, utilizes spherical Bessel functions to
solve two pairs of inhomogeneous equations for the components of radiation scattering from a dielectric
sphere.
For a particular radius of the spheres, resonance will occur at a corresponding frequency. In the
patent, with the sphere diameter set equal to 2 microns (2 x 10-6 m) one solution is found as an
example (col. 7, line 10). The resonant frequency is calculated to be about 9 x 1015 radians per second
(1.5 x 1014 Hz), which is the
corresponding frequency calculated
from the wavelength ( c = f λ ) that can
be assumed to classically resonate
with a sphere of that size, as also
found in the light spectrum chart
(Figure 10). This serves as one check
for the feasibility of the patent’s
prediction, since it is within a power of
ten of this answer for a microsphere.
The spacing between spheres, seen in
Figure 14, may resonate at a higher
harmonic.
The Cox report, supplied to this
author by Dr. Mead, ends with an offer
of general guidance, which is not
found in the patent, regarding
research in this area: “Much work still
remains in finding more resonances
and in studying other areas of the
theory. A source of EM radiation
having a broad enough range of
frequencies to achieve resonances
between two chosen spheres needs to
be selected. Then, one should analyze the beat frequency produced by the interaction of the two
Figure 10 - Electromagnetic Energy Conversion Chart
29
resonant waves, as well as the effect of separation distance of the two spheres on the beat frequency.
Finally, a method of rectifying this beat frequency should be established using currently available
equipment, if possible. It is also important to know how much energy is available at the resonant points.
As a practical matter, manufacturing processes must be investigated that would allow structures to be
fabricated with close enough tolerances to be of use.”134
It is not difficult to examine each of the above-mentioned recommendations offered by the
report, in order to assess the feasibility of this ZPE invention. First of all, the analysis used by the
inventors in the patent and the report depends upon one rather involved and somewhat obscure
approach to scattering from an older textbook. “The main area of concern addressed in this report is the
Figure 11 – Incident Wave and
Sphere
interaction of electromagnetic radiation with a dielectric sphere; i.e., the diffracting of a plane wave by a
sphere, more commonly known as Mie scattering.135 It is assumed that the sphere is made of a
homogeneous material and that the medium surrounding the sphere is a vacuum. The incident
radiation is assumed to be a plane wave propagating in the z-direction. Electrical vibrations of the
incident wave are assumed to occur in the x-direction, with magnetic vibrations in the y-direction (see
Figure 11). As explained in Stratton,136 “a forced oscillation of free and bound charges, synchronous
with the applied field, arises when a periodic wave falls incident upon a body, regardless of the sphere’s
material. This creates a secondary field in and around the body. The vector sum of these primary and
secondary fields gives the value of the overall field. In theory, a transient term must be added to
account for the failure of the boundary conditions to hold during the onset of forced oscillations.
However, in practice it is acceptable to consider only the steady-state, synchronous term because the
transient oscillations are quickly damped by absorption and radiation losses.”137
30
While this introductory viewpoint is sophisticated, it is also rudimentary, classical physics. The
calculations used by Stratton and Cox become cumbersome however, aimed toward the supposedly
obscure resonance between two spheres, though only one sphere is analyzed. The culmination of the
work solves for “RHO” (ρ) which is defined as the
propagation constant multiplied by the radius of
the dielectric sphere and alternately defined as
the radius times the frequency of interest divided
by the speed of light c.138 The report and patent
furthermore emphasize “resonant peaks,” seen
Figure 12 – FRHO graph
in Figure 12, which are claimed to be worthy of
special design considerations. However, it is
noted that these peaks of “FRHO” are less than a
power of ten from baseline, which, considering
standard engineering practice, will not warrant
special design attention. Considering feasibility
analysis, if each sphere successfully amplified
free energy from the vacuum, the improvement in
output from resonance beat frequency design
can only be a secondary consideration for quality
management to reduce waste and improve
efficiency after prototype manufacture, not a
primary focus patent and laboratory reports.139
Secondly, neither the patent nor the
report mentions the power density of the
scattered energy even once. It is assumed that
RHO is related to such a power consideration,
which is of primary interest for an energy
invention, but surprisingly, the concept of energy
density is not discussed in either publication.
These two issues create the distinct impression
that this invention is presented in such a way that distracts attention from the essential issue of
quantitative energy extraction.
With that preliminary assessment, the following physics analysis separates this theoretical
ZPE invention into four spheres of interest:
•
microsphere: micron-sized (10-6 m) electrolithography,
•
nanosphere: nanometer-sized (10-9 m) molecular nanotechnology,
•
picosphere: picometer-sized (10-12 m) atomic technology,
•
femtosphere: femtometer-sized (10-15 m) nuclear technology.
However, only the first two or three are amenable to electromagnetic analysis, with corresponding
wavelengths of interest. The fourth category requires quantum analysis. The relative comparison of λ >
R, λ = R, or λ < R may only differ if a resonance occurs near R = λ. The diameter (= 2R) of the sphere
is most often considered to resonate with the fundamental wavelength of interest but a factor of two
may not be significant in every case. In quantum mechanics however, de Broglie’s standing matter
waves correspond to the Bohr quantization condition for angular momentum, and are equal to an
integral multiple of the circumference (= 2πR) of an electron orbit of an atom.140
Scattering and absorption of electromagnetic radiation by a conducting or dielectric sphere
varies considerably in classical physics.141 Therefore, two additional distinctions, dielectric or conductor,
should also be considered for microspheres and nanospheres. A general benefit of the ubiquitous zero-
31
point electromagnetic radiation in regards to scattering is that with all of the spheres, no shadow or
transition regions need to be considered. Based on this nature of the ZPF, all parts of the surface of the
sphere considered are in the illumined region, which simplifies the analysis.
Regarding the patent’s reference to an increase of energy with frequency (col. 7, line 62), in
reality, the spectral energy density of the ZPF depends on the third power of frequency:142
hω 3
ρ o (ω ) = 2 3 = 3 × 10 − 40 f 3
2π c
eV/m 3
(16)
which is integrated further on to yield Equation (21) for a band of frequencies. It is noted that Equation
(16) is directly related to the third order dependence of radiation reaction, according to the fluctuationdissipation theorem.143
It is agreed that the general design criteria of the patent is feasible: “the spheres must be small
in direct proportion to the wavelength of the high frequencies of the incident electromagnetic radiation
at which resonance is desirably obtained” (col. 7, line 66).
Before proceeding with individual categories of spherical sizes and wavelengths, it is useful to
briefly review the “beating phenomena” as it is known in vibrational physics, whether in mechanical or
electromagnetic systems. Starting with two harmonic motions of the same amplitude but of slightly
different frequencies imposed upon a vibrating body, the amplitudes of the two vibrations can be
expressed as x1 = A cos ωt and x2 = A cos (ω + Δω)t . Adding these together and using a trigonometry
identity, it is found that the composite amplitude x = x1 + x2 is mathematically expressed as:144
x = {2A cos (Δω/2)t} cos (ω + Δω/2)t .
(17)
It is noted that Δω is normally a constant in most systems while ω may vary. Two observations for
Figure 13 – beating
phenomena
application to the ZPE patent being examined are the following:
•
the amplitude of the composite vibration is doubled (2A)
•
the beat frequency of the vibration is fb = Δω/2π Hz .
The period (wavelength) of the beating phenomena is T = 1/ fb (see Figure 13).
Also common in electronic and optical systems, where it is called “heterodyning,” the beating
phenomena permits reception at lower frequencies where a local oscillator is used to interfere with the
signal.
Microsphere Energy Collectors
The micron-sized sphere (microsphere) is already mentioned in the patent and in the Cox
report. Looking at some of the risks involved, it is assumed to have a radius R = 10-6 m but the second
32
adjacent sphere will unpredictably vary by at least 5%, due to manufacturing tolerances. A primary
example in the patent, general engineering considerations would question the advantage of designing
for a single beat frequency in this case, which tends to limit the bandwidth and energy output. Using
Figure 10 as mentioned previously, we find that a wavelength of a micrometer (micron) resonates with
a frequency of 1014 Hz, which is in the optical region. In this region, it would be prudent to utilize
photovoltaic (PV) technology for the converter 222 in Figure 14, which is already developed for the
conversion of optical radiation to electrical energy, which for silicon photovoltaic cells, peaks around 0.8
micron in optical wavelength.145 With that in mind, Figure 10 implies that the sphere might be a tenth of
a micron in size instead, with a wavelength in the UV region. Then, at the most, a 10% variation in size
will create a maximum beat frequency of about 1 x 1014
Hz. However, the feasibility of inducing a prominent beat
frequency with broadband ZPE electromagnetic wave
scattering by uncoupled dielectric spheres has to be
questioned in this case. Because the beating
phenomena, which only doubles the amplitude, will not
be significant in this regime, individual spheres
constructed adjacent to a micron-sized PV converter,
may be preferable, as seen in Figure 14 from the patent.
Scattering contributions by these microspheres
can be analyzed from classical electrodynamic
equations that apply. The range λ > R is scattering of
Figure 14 – Mead’s semiconductor spheres
electromagnetic waves by systems whose individual
dimensions are small compared with a wavelength, which “is a common and important occurrence.”146
Without polarization of the incident wave, since ZPE radiation is ubiquitous, it will not contribute to
dipole or multipole formation on the sphere. Assumptions include a permeability μ = 1 and a uniform
dielectric constant Є which varies with frequency. Energy output is calculated by the total scattering
cross section σ.147 With units of area, σ is “an area normal to the incident beam which intercepts an
amount of incident power equal to the scattered power.”148
The total scattering cross section of a dielectric sphere for λ > R is,
4
6
σ = ⅓ 8π b R
Figure 15 – Dielectric constant
over range of 1 to 100 in
variation with frequency.
the limit of 1 (where the permittivity equals Єo ).
│Є – 1│2
│Є + 2│2
(18)
where wave number b = ω / c = 2π /λ.
The dielectric constant Є is actually the
“relative dielectric constant” which is a ratio of
substance permittivity to the permittivity of
free space Єo. In order to appreciate the
range of values that Equation (18) may
assume, it is noted that “At optical
frequencies, only the electrons can respond
significantly. The dielectric constants are in
the range Є = 1.7 – 10, with Є = 2 – 3 for
most solids. Water has Є = 1.77 – 1.80 over
the visible range, essentially independent of
temperature from 0 to 100C.“149 With this
information in mind, a graph of the behavior
with frequency is also shown in Figure 15. A
declining Є with frequency can only make
Equation (18) even smaller as Є tends toward
33
As an example of the total cross section for scattering by a relatively good dielectric, Є = 3 can
be chosen. Then, with f = 1014 Hz and R = 0.1 x 10-6 m (thus keeping λ > R), Equation (18) is found to
yield σ = 2.6 x 10-17 m2. Dividing σ by the actual cross sectional area of a microsphere ( πR2 ) for
comparison, scattering by a dielectric sphere of optical frequency electromagnetic radiation yields a
loss of about 8 x 10-6 in power.
In comparison, for λ > R, small conducting spheres have a total scattering cross section that is
significantly larger, where
σ = ⅓ 10π b4 R6 .
(19)
There is an advantage of using conducting spheres in place of the dielectric spheres which is
more significant than designing for the doubling effect from possible beat frequencies. The cross
section σ for a one-tenth micron-sized conducting sphere (R = 0.1 x 10-6 m) with visible light incident (f
= 1014 Hz) yields about 2 x 10-16 m2 for λ > R.150 Dividing this as before by the actual cross sectional
area yields only 6 x 10-5 loss of power or ten times
better than the dielectric scattering cross section.
While both of these total cross section
calculations still may seem very low, there seems to
be an explanation for it. Since they were still within
a power of ten from λ = R, Figure 16 shows there is
an interference scattering effect for plane waves,
within a few wavelengths of this region. Utilizing the
spherical Bessel function expansion for a plane
wave, similar to the inventor Mead, the solution with
amplitudes and phases is found for the boundary
condition that the wave function is zero at R = a but
the radial velocity of the wave is zero at R = 0. As
seen in Figure 16 (the textbook uses Q for total
cross section), the surprise is that in the region of λ
Figure 16 – Total scattering cross section Q for a
= 2πR and smaller (<1 on the abscissa), the total
plane wave scattering from a sphere R = a.
cross section becomes very small, tending to zero.
The graph, however, reflects the boundary conditions used, such as the radial velocity vr of the ratio S
(of scattered intensity to incident intensity) = 0, the total cross section calculation with the proper Bessel
function tends toward the limit of 2πR2 for λ <<R, which is twice the actual cross sectional area.
However, for very long wavelengths compared to the radius (λ >>R) the total cross section for plane
wave scattering by a sphere tends toward 4πR2 which is four times the actual cross sectional area.151
Also confirmed from Figure 17, based on the same text with a Bessel function treatment of a
plane wave incident (from the left) on a rigid sphere,
the scattered intensity grows larger with smaller
wavelength, instead of exhibiting a trend toward
resonance when λ ≈ R, tending to be “spherically
symmetrical” in the limit where bR Æ 0, S Æ 1, and σ
Æ 4πR2. These figures seem to contradict the
inventor’s assertion of a ZPE electromagnetic
resonance with a microsphere and any number of
microspheres in close proximity. Furthermore, the
penetration of electromagnetic waves throughout
dielectric spheres is another complication which is
treated in detail in the above-mentioned theoretical
physics text, including a complex index of refraction
when required, to account for transmission,
Figure 17 – Scattered intensity for a plane wave
scattering from a sphere R = a.
34
reflection, and absorption.152 These two issues diminish the feasibility of the inventor’s
microsphere design significantly.
In the region of λ <R, classical ray theory applies since the wavelength is short compared to the
radius of curvature. Fresnel equations can also be utilized, treating the surface as locally flat.153 This
argument also leads to the standard description in physics of specular reflection.
To show the value of Bessel function analysis of plane wave scattering and the strong
directional dependence, a graph of the differential cross section is plotted in Figure 18. Considering the
previously mentioned advantage of using conducting spheres of the micron size, the analysis is also
more straightforward. Under these circumstances, the tangential magnetic fields and normal electric
fields of the electromagnetic wave will be approximately equal to the incident wave.154 The differential
backward scattering of the incident radiation, for λ < R and θ < 10/bR is found to be,
dσ
= R 2 (bR
dΩ
)
2
J 1 (bR sin θ )
bRsin θ
2
(20)
where J1 is a Bessel function of the first kind of order one. The forward differential scattering for θ >>
1/bR (higher θ angles) is simply R2/4. A plot of Equation (20), for the smaller angles, is the dashed line
in Figure 18, with the exact solution as the solid line. Destructive interference is noted where it dips
below unity.155 The peak in
the graph of Figure 18
indicates a strong reflection
back-scattering
for
a
conductive sphere. This is a
common
phenomenon
Figure 18 – Unpolarized scattering from a
conducting sphere as a function of
since silver, a very good
scattering angle θ in the short-wavelength
conductor, is used often for
range of λ < R. For convenience, bR = 10
coating glass to create
for this plot.
mirrors. The conductive
surface allows the electric
field
vector
of
the
electromagnetic wave to
oscillate
freely
upon
contact, with very little
resistance, thus creating
the reflective wave.
Ordinate axis units: 4 dσ
R2 dΩ
Such
electromagnetic
radiation
scattering
is
distinguished
from
Thomson
scattering,
Rayleigh
scattering,
Coulomb
scattering,
Compton and Rutherford
scattering, which also use
cross section formulae as
well. Each of these, more
common
with
particle
scattering, will be discussed
in the following sections.
It should be emphasized that the same two σ limits discussed above, 2πR2 and 4πR2, for small
wavelengths (λ <<R) and large wavelengths (λ >>R) respectively, are also derived in quantum
35
mechanics using the method of partial waves for scattering of wave packets by a perfectly rigid sphere
and thus will also be applied in the further sections to follow.156
For feasibility consideration of energy extraction, to collect and transduce the total scattered
ZPE radiation from the vacuum flux, it would be necessary to place one sphere at the focus of an
evacuated, reflecting 3-D ellipsoid cavity with the PV converter at the other, for example, instead of the
spherical cavity the inventors refer to. However, in the interest of maximizing energy output per volume,
it may be more convenient to engineer sheets of single spheres placed in alternate planes between
planar PV converters, which may unfortunately limit the available ZPF frequencies.
An important calculation for each sphere of interest is to find whether significant scattered zeropoint energy is available at these wavelengths. Therefore, the spectral density of ZPE Equation (16)
is integrated as,157
(21)
For the wavelength range of 0.4 to 0.7 microns (micrometers) in the visible light band, using Equation
(8), the radial frequencies can be generated for the integrated energy density equation. Substituting
these for ω2 and ω1 we find an energy density of only 22 J/m3 or 22 microjoules/cc which equals
approximately 0.24 eV/μm3 (electron volts per cubic micron).
To create a simple standard calculation for the frequency band of each sphere of interest, ω2 is
chosen to correspond to the radius R and ω1 is chosen to be 1/10 of that frequency. For a microsphere,
with λ = R = 10-6 m, the spectral energy density from Equation (21) is ρ(ω) = 0.62 J/m3 or 3.9 eV/μm3
for the decade range: Δf = 3 x 1013 to 3 x 1014 Hz. From Figure 10, this energy density is also
comparable to the photon energy (2 eV) in the visible band.
Nanosphere Energy Scatterers
In the region of λ > R for the scattering by these nano-sized spheres (nanosphere) the classical
electrodynamic equations still apply. However, with a radius R of the sphere considered to be 10-9 m,
the effect on the ZPF spectral energy density is quite dramatic. In Figure 22, it is noted that 1 nm is in
the keV region. A resonant correspondence with the sphere diameter of 2 x 10-9 m equals a full
wavelength antenna, the resonant frequency will be in the range of 1 x 1017 Hz. The spectral energy
density of ZPE at this frequency is substantially more promising. Using Equation (21), we find that the
ZPE spectral energy density is 6.2 x 1011 J/m3, which is a billion times more energy per cubic meter
than was available from the ZPF for the micro-sized spheres. Converting to electronvolts per cubic
nanometer, it is interesting that the ZPF offers about 390 eV/nm3 which is three orders of magnitude
more energy than available to the micron-sized sphere. The advantage as well is that a billion of these
spheres will fit into a cubic micrometer, if a collection was found to be coherently constructive with
regards to scattering. Vacuum polarization is probably more pronounced at the nanometer
dimensions, yielding more ZPE virtual particles which would be expected contribute more significantly
to scattering off of nanospheres.
Evaluating Equation (19) at this resonant frequency and radius, it is found that for a conducting
nanosphere, the scattering cross section σ = 1 x 10–15 m2 for the region λ > R. Comparing with crosssectional area πR2 for the nanospheres, it is found to be 318 times its cross-sectional area πR2. (The
ratio of σ to spherical surface area is also constant σ /4π R2 = 83). This demonstrates that the
scattering cross section σ is geometrically correlated to the object’s actual cross-sectional area.
For the consideration of λ ≈ 2R, resonance is still not expected to affect the amplitude of
scattered radiation appreciably.
36
For the consideration of λ < R the scattering profile seen in Figure 18 would still apply because
quantum mechanical effects become important only when hf ≈ mc2. This may be anticipated for the
femtosphere.158
The present state of the art for engineering capabilities in the microsphere and nanosphere
regions is illustrated in Figure 19. Called “nanoboxes,” they are electrically conductive single crystals of
silver, produced at the University of Washington, with slightly truncated edges and corners. “Each box
was bounded by two sets of facets (eight triangular facets and six square ones), and any one of these
facets could lie against a solid substrate. The inset shows the SEM image of an individual box sitting on
a silicon substrate against one of its triangular facets, illustrating the high symmetry of this polyhedral
hollow nanoparticle.”159 Octahedra and tetrahedra, such as the inset have also been produced, which
approach the patent-proposed ideal of a nanosphere. The white scale
bar at the bottom of Figure 19 is 100 nm in length for comparison. For
17-min and 14-min growth times, the nanocubes had a mean edge
length of 115 ± 9 and 95 ± 7 nm, respectively. For the sake of the
feasibility discussion, regarding the microsphere’s difficulty of
predictable beat frequencies, it is noted that the tolerances quoted
here are between 7% and 8%. Thus, the benefit of a single beat
frequency production of two adjacent silver nanopolyhedrons is
judged to be not feasible at either microsphere or nanosphere sizes
because of the large manufacturing errors. Nanocubes with sides as
Figure 19 – nanoboxes
small as 50 nm have also been obtained, though some of them were
not able to evolve into complete truncated cubes.
Regarding the scale of 1 nanometer in diameter, such as the nanosphere that is proposed, the
error control may not require a higher tolerance range than quoted above. As seen in Figure 20, if
individual molecular crystals were used for 1 nm range, they do not vary widely in size.160 A sphere of
carbon-60, for example, would be a real possibility, though it is not highly conductive. If metal
nanopolygons are used, it is noted that “nonspherical gold and silver nanoparticles absorb and scatter
light of different wavelengths, depending on nanoparticle size and shape.”161
Interestingly, gold and silver nanoparticles have been
used as sensors, since they have surface-enhanced Raman
scattering and other optical effects peculiar to the ~10- to 100-nm
range.162 Instead, using heavy metal atoms, such as Polonium with a
diameter of 0.336 nm should be considered in this section because of
superior spherical shape and reproducibility. Polonium may also be
an interesting candidate because it is the only element known to
crystallize in a primitive cubic unit cell under room temperature
conditions.163 Therefore, the interatomic spacing is also very well
known. ZPE virtual particles, or equivalent ZPE electromagnetic
radiation, would not be expected to play a large part in scattering off
polonium atoms however. Instead, they already are known to
contribute to the Lamb shift of the 2p electron levels, with about 1.06
GHz worth of energy. Furthermore, virtual particle scattering
“contributes the same energy to every state,” consisting of
e2A2/2mc2 in the nonrelativistic theory with the Hamiltonian, where A
is the vector potential.164 Beat frequencies would be unlikely and very
difficult to engineer with polonium atoms since the atoms would
normally share the same energy, being at the same temperature, etc.
Figure 20 – molecular picture
37
Picosphere Energy Resonators
In the picosphere range, it is more likely that some of the key elements of this patent may be
more effectively applied. One of the reasons for this is that up until this point, there has not been a
necessity for lower frequency scattering. To review some of the transduction methods available, Figure
21 shows some of the standard devices for transducing ionization into electricity. Note that ionizing
radiation can also consist of electromagnetic X-rays or
gamma rays since there is sufficient energy at these
Figure 21 – Ionization transducers
frequencies to cause ionization. The method of ionizing
transduction relies upon the production of ion pairs in a
gas or solid by the incidence of radiation. The applied
electric field in Figure 21 is an excitation voltage (Exc.)
used to separate the ionized positive and negative
charges to produce an electromotive force.165 For the
picosphere range, it is also expected that small individual
atoms can be arranged to meet the specifications for the
patent more effectively since nature has much better error
tolerances than engineers can manufacture artificially.
The high frequency electromagnetic spectrum is
reproduced in Figure 22, which picks up where Figure 10
left off, with wavelength decreasing from left to right.166
The picosphere with a radius of 10-12 m (1 pm) and a
wavelength equal to its diameter, corresponds to a
frequency of 1.5 x 1020 Hz using Equation (8). Using Einstein’s equation E = hf, the photon energy at
that frequency can be found to be about 650 keV which is useful to compare with the spectral energy
density. Using Equation (21), we calculate a spectral energy density of 6.2 x 1023 J/m3 or 390 keV/pm3.
In the range of λ > R the scattering cross section σ = 1 x 10–21 m2 is in the same proportion of
318 times sphere cross sectional area.
Figure 22 – Electromagnetic spectrum
38
At the resonant wavelength of λ ≈ 2R, the amplitude of
scattering can be expected to be higher. It is also anticipated that
here is where the concept of beat frequency may be applied
more conveniently, with greater precision than in either larger
category. However, since all atomic radii vary between 50 pm
(e.g., Helium) and 660 pm (e.g., Cesium), the picosphere with a
proposed radius of 1 pm has to be declared to be impractical and
therefore, not feasible.
In the range of λ < R the scattering seen in Figures 16
and 17 would still apply. The diffraction pattern is also very
predictable. The intensity distribution of X-ray diffraction could be
correlated to the theoretical scattering off a sphere from Equation
(21). An example is seen in Figure 23 where the wavelength of
the X-rays is 71 pm and the target is an aluminum atom, which
has an atomic radius of 182 pm.167
Figure 23 – X-ray diffraction
If a smaller target on the order of a picosphere were used, it is
expected that the scattering pattern would be the same for λ < R.
In this region, the need for a heterodyned frequency might
emerge if, for example, the ionization transducers of Figure 21 were not configured for high efficiency
capturing of the ZPE scattered radiation. However, the production of a beat frequency that also
resonates with the geometry of an array of atoms may be problematic, for two reasons. The array
would preferably need to be a 2-D sheet only one atom thick, such as thin metal foil used for diffraction
studies, to prevent destructive interference of the ZPF scattering. Secondly, the real barrier to creating
a useful ZPE beat frequency atomic array is producing picospheres that vary reliably in one part in one
thousand with a maximum error tolerance of one part in ten thousand. An avenue of speculative
physics would require the engineer to estimate the diameter of a suitable metal atom in the ground
state and pursue a manufacturing procedure to excite alternate adjacent atoms to a very long
metastable state, which is known to expand its size, much like Ryberg atoms.168 Hypothetically, this
ideal situation would achieve a small difference in diameter of adjacent atoms sufficient to produce beat
frequencies of resonant scattered ZPE.
Utilizing the Fermi-Thomas model of the atom, most atomic radii can be approximated by
a ≈
1.4 ao / Z⅓
(22)
where Z = atomic number and ao = h2 / me2, the hydrogenic Bohr radius.169 Taking an excellent
example of two atoms with similar size, platinum (Pt) and gold (Au) would be good candidates since
they are next to each other on the periodic table and relatively inert, Noble metals. It is presumed that
the diameter may resonate with a full wavelength, with 183 pm and 179 pm as the radii for Pt and Au
respectively.170 In that case, 8.20 x 1017 Hz is the corresponding Pt frequency and 8.37 x 1017 Hz is the
corresponding Au frequency, both in the soft X-ray band. Subtracting the two frequencies, the beat
frequency would theoretically be a difference of 1.83 x 1016 Hz, moving it down into the UV band. If the
conversion of UV incident electromagnetic energy is more efficient than transducing soft X-rays, then
this method would offer a chance to collect ZPE, so long as the arrangement of multiple pairs of Pt and
Au atoms could constructively interfere at their beat frequency. However, the wavelength of 1.83 x 1016
Hz is about 16 nm, which forces the placement of individual atomic pairs to be fairly distant from each
other, compared to their size. With only a 2% difference in diameter, the beat frequency difference
yields a power of ten difference for lower frequency detection, as the Mead-Cox resonant microsphere
analysis of Figure 11. The improvement in amplitude from resonance would reasonably be only a
power of two, unless a resonant cavity was used as well.
39
Another example, representing the smallest atomic pair that is available for this experiment, is
hydrogen (H) and deuterium (D), an isotope of hydrogen with one proton and one neutron in the
nucleus. The Bohr radius ao for hydrogen is 53 pm and the atomic radius of deuterium is about the
same. In fact, the Hα emission lines (Balmer series) for deuterium and hydrogen are 656.10 nm and
656.28 nm respectively, a
difference
of
only
Figure 24 – Upscattering energy gain
0.03%.171 Such a similar
size will force the beating
frequency to be more
than a power of ten
difference,
which
apparently is viewed as
an advantage by the
patent holders. For such
gaseous
atoms,
the
phenomenon
of
“upscattering” might be
achieved with this gas at
a finite temperature T with
a
Maxwell-Boltzmann
velocity distribution if the incident ZPE virtual particles fell into a regime of low energy up to about 10
kT.172 This implies that it is possible for the incident particle to gain energy in a scattering collision. In
the situation where the hydrogen or deuterium nuclei might be at rest, the scattering probability P(EI Æ
Ef ) inversely depends upon the incident particle energy Ei. However, for elastic scattering in a
hydrogen (proton) gas, the scattering probability depends on the final particle energy Ef and is not zero
even for Ef > Ei. In Figure 24, a graph is shown of the scattering probability for scattering of a proton
gas with various incident particle energies. With resonance considerations seen in Figure 25 added to
the design as well, such a regime might be a test, with a minimum of risk, for the Mead spherical
collector concept in an atomic, picosphere region. However, with or without a successfully amplified
beat frequency, the upscattering of virtual particles from a proton gas may still have inherent flaws for
two reasons: 1) most such proton gas experiments have been conducted only with low energy incident
neutrons; 2) “the dissipative effect of radiation reaction precludes spontaneous absorption of energy
from the vacuum field” which normally applies only to an atom in the ground state.173 Yet, the gain of
one to two times the incident EI = kBT may be valuable to the energy equation as the gas transfers
energy to the incident particles, even if the probability drops to 50%, since theoretically an abundant
number of virtual particles are available. At room temperature (T – 300K) for example, 1 kBT = 0.026 eV
which is about 1013 Hz or an
Figure 25 – Broadening of
infrared terahertz frequency.
the resonance peak with
increasing temperature
40
In Figure 25, an example of a capture resonance is shown at temperature T1, where the
average cross section dramatically increases for a certain resonant incident energy Eo. Another aspect
of temperature increase is also graphically demonstrated. This is called “Doppler broadening” caused
by the Doppler shift in frequency as a thermally excited atom moves away from or toward the incident
particle with greater temperature-dependent speed.174 Therefore, an increase in temperature causes
the increased cross section of a resonant peak to be lost. Lower temperatures are important for
preserving the advantage of resonance.
Thus examining the options for the resonant sphere, the two atomic pairs of deuterium and
hydrogen are the best beating examples in the picosphere region, still demonstrating major unknowns
in the “beat frequency” design concept of the Mead patent. At the present state of nanotechnology
development however, the picospheres cannot be manufactured, except by atomic force “pick and
place” devices.
Quantum Femtosphere Amplifiers
With the examination of the femtosphere (R = 10-15 m = 1fm) there are a number of phenomena
that synchronize so well with this dimension that the patent being examined seems to be more
compatible with the nuclear particle than any other size sphere. The first obvious advantage is the
spectral energy density of Equation (21) which is found to be 6.2 x 1035 J/m3 or 390 MeV/fm3. This is
also interesting in that the quantum mechanical realm applies where hf is about the same as mc2.
Testing for this condition, both energies are calculated with a wavelength of 2 x 10-15 m and a
corresponding frequency (see Figure 22) of 1.5 x 1023 Hz. The Einstein formula for photon energy of
the femtosphere is
E = hf = 9.9 x 10-11 J = 619 MeV .
(23)
To determine the mass of the femtosphere, it is known that the radius of either the proton or
neutron is about 8 x 10-16 m.175,176 This is remarkably close (within 20%) to the conceptual femtosphere
radius R of 1 fm. Therefore, it is reasonable to use the average mass of either nuclear particle (1.7 x
10-27 kg) in the Einstein equation for mass-energy, to find the energy equivalent of the femtosphere’s
mass:
E = mc2 = 1.5 x 10-10 J = 938 MeV .
(24)
Comparing Equations (23) and (24), they are the same order of magnitude, so it is determined that
quantum mechanical rules apply in this region. The classical equations for energy and scattering
cross section are still applicable. However, they may be regarded as classical approximations, in view
of the correspondence principle, to quantum mechanical phenomena. “The important quantum effects
are (1) discreteness of the
possible energy transfers, and
(2) limitations due to the wave
nature of the particles and the
uncertainty principle.”177
In this femtosphere
range, Rutherford scattering is
applicable. The total nuclear
Rutherford scattering cross
section is
σ = πR
(2zZe )
2 2
2
(hv )2
,
(25)
where z is the number of
charges (particles) in the
41
incident at a velocity v and Z is the number of charges (particles) in the target. For example, at high
velocities, even for incident virtual photon radiation, the total cross section can be far smaller than the
classical value of πR2, which is its geometrical area.178 The parenthetical terms in Equation (25) can
result in a reduction of 10-24 times the geometrical area π R2 of the target for an incident photon at the
speed of light.
For this size of target, due to vacuum polarization, it is important to mention that more incident virtual
particles from the vacuum, as discussed in Chapter 1 (with an artist rendering in Figure 3), will also be
present for a charged femtosphere. Therefore, the de Broglie wavelength of the incident particle will
also be important, treating the ZPF virtual particles on the same level as electromagnetic waves:
λ = h/p = h/mv
.
(26)
The de Broglie requirement of quantum mechanics, postulated in 1924,179 thus affects the possibilities
for energy generation for the Mead patented design. “For a nucleus of finite size…the de Broglie
wavelength of the incident particle does enter…The situation is quite analogous to the diffraction of
waves by a spherical object.”180
Vacuum polarization will also enhance the natural electromagnetic radiation from the vacuum
for the femtosphere. Since double slit experiments with particles like electrons and neutrons
demonstrate the wave phenomenon of diffraction, femtosphere particles can also be regarded as “wave
packets.”181
This type of scattering utilizes the continuously distributed energy eigenvalues of quantum mechanics
which consider the boundary conditions at great distances from the collision. The scattering is treated
here only as elastic scattering, so there is no absorption by the target. This is different from
photoelectric scattering or Rayleigh scattering, which are inelastic.
For the region of λ > R this can be represented by the low energy limit where 2πR << λ (the
circumference is much less than the wavelength). For the femtosphere, the total cross section is
approximately σ ≈ 10-30 m2 in this low frequency, long wavelength region.
For the region of λ ≈ 2R or 2πR, there is a uniquely quantum mechanical phenomenon of
resonant scattering called “resonance fluorescence” that applies “to the absorption of radiation by an
atom, molecule, or nucleus in a transition from its ground state to an excited state with the subsequent
re-emission of the radiation in other directions in the process of de-excitation.”182 The reaction of the
target when the frequency of the incident equals the binding energy of the target, the scattering
becomes very great, exhibiting a formal resonance peak seen in Figure 26.
Note that a single femtosphere, such as a free neutron or proton would not possess the
requisite binding energy for this type of oscillator resonance. In addition, this process reveals an
inelastic
form
of
scattering
but
the
dramatically
increased
cross section apparent in
the resonant peak of
Figure 26 more than
Figure 26 – Total cross
makes up for any energy
section resonance
lost in absorption and refluorescence for scattering
emission.
Resonance
radiation by an oscillator
fluorescence brings a
number of phenomena
into play that are seen in
Figure 26, such as
Thomson
scattering,
which is scattering of
radiation by a free
42
charge. It can be X-rays by electrons or gamma rays by a proton for example.183 Thomson scattering
occurs along a baseline of higher frequencies in Figure 26 above ωo,
where the cross section is
8ππ4
σT =
3m 2 c 4
(27)
The Thomson cross section of Equation (27), evaluated for a target electron, yields 6.6 x 10-25 cm2 for
σT where e2/mc2 = 2.8 fm, the classical electron radius.
By comparison, the Rayleigh scattering (which causes the atmosphere to take on a blue color)
cross section has a dependence on the fourth power of the incident frequency. Thus, the highest visible
frequency (blue color) has a much larger scattering cross section and consequently, a stronger
interaction with air molecules, including a wide scattering angle. Both phenomena illustrate the
dominance of cross section scattering terms with cubic and quartic exponents.
Deuteron Femtosphere
One example of an intriguing femtosphere oscillator is the deuteron (a proton bound to a
neutron in close contact), which also demonstrates resonant fluorescence. It would satisfy the
requirement of “binding energy” for the target and is also treated as an oscillator. However, it should be
mentioned that it is unlikely that the deuteron would exhibit beat phenomena, since the wave functions
overlap making the deuteron behave as one nucleus (ionized deuterium), with a single resonant
frequency and a radius of about 2 fm.184
Recalling that the beat frequency design of the Mead patent is simply a means to downshift the
radiated frequency, it is also possible to use the standard electrical engineering approach instead.
Frequency converters, for example, utilize a “local oscillator” which mixes with the incoming signal to
produce a subtracted intermediate frequency one or two orders of magnitude lower, for the same
purpose. Once the resonant frequency of the deuteron is determined to be beyond the useful energy
transduction range, an engineering recommendation therefore, would be to find a lower local oscillator
in the same range, so that a substantially reduced intermediate frequency can be produced.
The deuteron has one bound state ( l = 0 ) of a proton and neutron with binding energy of Eb =
2.23 MeV. The more preferred state ( 75% ) is where the spin ½ of the proton and neutron are parallel
(triplet state). The cross section for the deuteron is
2πh 2 m
σ=
E − Eb
(28)
Equation (28) is about 70 x 10-24 cm2 for the singlet (antiparallel) state and about 20 x 10-24 cm2 for the
triplet state, which computes to 550 times and 157 times the geometrical cross sectional area,
respectively.
With resonance fluorescence, the condition is in a sense an almost bound state that isn’t below
zero energy to be a true bound state (see the dashed line levels in Figure 27). If the potential V(r) is an
attractive well, then the effective potential is,
Veff = V(r) + h2 l (l+1) / 2mr2
(29)
where the integer angular momentum quantum
number, l > 1. “Resonances are the ‘bound states’
of the well at the positive energy, indicated by the
dotted lines...What happens in scattering at a
43
resonant energy is that the incident particle has a large probability of becoming temporarily trapped in
such a quasi-bound state of the well; this possibility increases the scattering cross section.”185 In Figure
27, the depth of the potential well for the deuteron must be Vo = 36 MeV for the deuteron.186
With that introduction to resonance with the deuteron, it should be mentioned that it is also an
advantageous oscillator since the binding energy of Eb = 2.23 MeV corresponds to an X-ray frequency
of fb = 5.4 x 1020 Hz, instead of the gamma ray frequency of
Figure 27 – Effective potential creating an almost
1023 Hz that should resonate with the diameter of a
bound state for a resonance condition of an attractive
femtosphere. Thus, the deuteron binding energy satisfies the
potential
need for a lowering of the resonant frequency for
transduction purposes, voiced in the Mead patent. The cross section is complicated by the existence of
a singlet and triplet state depending on the proton and neutron spin direction. “There are no bound
excited states of the deuteron. Neutron-proton scattering experiments indicate that the force between n
and p in the singlet state (antiparallel spins) is just sufficiently less strong than in the triplet state to
make the deuteron unstable if the spins are antiparallel…there is a small, measurable quadrupole
moment.”187
For the region of even smaller sizes, beyond the femtosphere resonance, where λ < R, the
cross section can be represented by the high energy limit where R >> λ. Here the scattering by a
perfectly rigid femtosphere can be approximated, as mentioned with the microsphere, with a total cross
section of
σ
≈
2πR2
(29)
188
which is twice the actual geometrical cross section area. The reason for the apparently anomalous
result of Equation (29) is that the asymptotic form of the wave function is composed of the incident and
the scattered wave, which also experiences interference between the two partial waves. “However, so
long as 2πR/λ is finite, diffraction around the sphere in the forward direction actually takes place, and
the total measured cross section…is approximately 2πR2.“189
Electron Femtosphere
The electron may actually be the preferred femtosphere for many reasons. Its classical
radius ro is calculated to be 2.8 x 10–15 m or 2.8 fm and is suitable for a Mead patent test. As seen in
Figure 3, the electron, like the proton, offers a steep electrical gradient at its boundary that creates a
decay or polarization of the vacuum locally. It is expected that electron charge clusters like Cooper
pairs or bigger boson charge bundles can offer a substantially enhanced vacuum activity in their
vicinity. The patents of Ken Shoulders (US #5,018,180) and Hal Puthoff (US #5,208,844) on charge
cluster devices discuss the potentials of such an approach but they seem to lack sufficient engineering
skills to control their volatility. Therefore, an ion trap or “force field” confinement process is required. In
fact, Hans Dehmelt at the University of Washington used such a trap to compress 1000 electrons into a
300 micron spherical plasma drop in order to study them.190 When dealing with high speed electron
cluster production, it is also reasonable to suggest the use of multiple toroid inductive couplers to
convert the kinetic energy into electricity.
QED vacuum effects such as the coupling of the atomic electron to the vacuum electromagnetic
field show that the electron is more intimately connected to the vacuum flux than most other particles.
“The zero-point oscillations of the field contribute to the electron a certain amount of energy…Efl ~
e2h/4mca2,” with an upper bound of hfmax = 15 MeV for a free electron.191 The coupling term for the
atomic electron in the Hamiltonian is (e2/2mc2 )A2 where A is the vector potential and the parenthetical
modifier is familiar from Equation (27) as half of the classical electron radius. “Since this term does not
involve atomic operators, it contributes the same energy to every state” in the atom.192 Besides the
ground state contribution, called the Lamb shift, it is true that every other electron level is also shifted
upwards from vacuum flux energy or virtual particles. For this reason alone, it should be emphasized
that extraction of energy from the vacuum is already occurring in every atom throughout the
universe, since every atomic electron and every free electron is ZPE-powered. However within the
44
atomic system, “the effects of the vacuum field and radiation reaction cancel, so that the ‘spontaneous
absorption’ rate is”193
A12 = RVF - RRR = ½ A21 - ½ A21 = 0
(30)
where A12 is the Einstein A coefficient for the electron transition from the ground state to the first atomic
energy level. The spontaneous emission rate sums the rate of energy absorption from the vacuum field
RVF and the radiation reaction rate RRR to equal the Einstein A coefficient.
The
energetic
scattering of the vacuum
flux on a free electron,
clearly seen in Figure 3,
may
be
optimally
amplified in the gaseous
state of a plasma, such as
within the confines of an
ion trap. This author
collaborated
in
the
construction of such a
trap, which proved that
electron and ion densities
can be increased with
such a trap, as the
electrons are retained in
one place for measurements and energy extraction.194 Such an apparatus may also work well for
charge clusters, after applying inductive toroidal braking to their kinetic energy. For an applied voltage
of 300V and vacuum pressures of at least a microTorr, the concentration of ions ranged between 108
and 1010 ions per cc. As seen in Figure 29, the voltage profile or potential distribution inside the grid
with the presence of negative space charge from the Thoriated filaments exhibits a large concentration
of electrons. Assuming that charge clusters cannot be trapped by any other means without destroying
them, the nonresonant ion trap should provide a reliable method for study and possible energy
extraction if an additional collection and amplification method for the femtosphere is optimized and
implemented.
Figure 28 – Nonresonant ion trap with voltage applied to grid, driver plate, and
extraction plate. Thoriated filaments supply electrons.
Weisskopf notes that if the electron is assumed to be a sphere of radius a, then only waves with
a wavelength λ /2π > a will act upon the electron, while the wavelengths λ /2π >> a will not be that
significant. The upper bound of hfmax assumes an electron radius of a = c/fmax while the number of
vibration modes of the ZPF gives rise to a value of a ≈
ro( hc/e2)½ so that “the fluctuation energy seemingly
pushes the electron radius to even greater values…”195
Casimir Force Electricity Generator
A fascinating example of utilizing mechanical
forces from the Casimir effect and a change of the
surface dielectric properties, to intimately control the
abundance of virtual particles, is an optically-controlled
vacuum energy transducer developed by a Jet
Propulsion Lab scientist.196 A moving cantilever or
membrane is proposed to cyclically change the active
volume of the chamber as it generates electricity with a
thermodynamic engine cycle. The invention proposes to
use the Casimir force to power the microcantilever
beam produced with standard micromachining
Figure 29 – Potential distribution in ion trap
45
technology. The silicon structure may also include a microbridge or micromembrane instead, all of
which have a natural oscillation frequency on the order of a free-carrier lifetime in the same material.
The discussion will refer the (micro)cantilever design but it is understood that a microbridge or flexible
membrane could also be substituted. The invention is based on the cyclic manipulation of the
dimensions of Casimir cavity created between the cantilever and the substrate as seen in Figure 30.
The semiconducting membrane (SCM) is the cantilever which could be on the order of 50-100 microns
in size with a few micron thickness in order to obtain a resonant frequency in the range of 10 kHz, for
example.
Two monochromatic lasers (RS) are turned on thereby increasing the Casimir force by
optically changing the dielectric properties of the cantilever. This frequency dependence of a
dielectric constant, can be seen in Figure 15. It can vary with frequency by a few orders of magnitude
inversely proportional to the frequency. The standard analysis of cavity modes usually identifies the
resonant modes of the cavity, dependent on
the boundary conditions.197,198 However, Pinto’s
pro-active approach is to excite a particular
frequency mode in the cavity. In doing so, an
applied electrostatic charge (Vb) increases as
the cantilever is pulled toward the adjacent
substrate (SCP) by the Casimir force. Bending
the charged cantilever on a nanoscale, the
Casimir attractive force is theoretically
balanced with opposing electrostatic forces, in
the same way as Forward’s “parking ramp” of
Figure 8. As the potential difference to the
cantilever assembly is applied with reference to
a conducting surface (CP2) nearby, the
distance to this surface is also kept much larger
than the distance between the cantilever and
the substrate (SCP). Upon microlaser
illumination, which changes the dielectric
properties of the surface and increases the
Casimir force, there is also predicted an
Figure 30 – Pinto’s optically controlled vacuum engine
increase in electrostatic energy due to an
increase in capacitance and voltage potential.
Therefore a finite electrical current can be
extracted and the circuit battery is charged by an energy amount equal to the net work done by
the Casimir force. Pinto estimates the Casimir force field energy transfer to be approximately 100 to
1000 erg/cm2.199 Converting this to similar units used previously, this Casimir engine should produce in
the range of 60 to 600 TeV/cm2 (teraelectron volts per square centimeter) which is also equal to 0.01 to
0.1 mJ/cm2 for every thermodynamic engine cycle diagrammed in Figure 31.
Analysis of the Casimir engine cycle demonstrates its departure from hydroelectric, gaseous, or
Figure 31 – Thermodynamic
engine cycle of Pinto’s vacuum
energy transducer where
FCas = Casimir force
46
gravitational systems. For example, the Casimir pressure always acts opposite to the gas pressure
of classical thermodynamics and the energy transfer which causes dielectric surface changes “does not
flow to the virtual photon gas.”200 Altering physical parameters of the device therefore, can change the
total work done by the Casimir force, in contrast to gravitational or hydroelectric systems. Unique to
the quantum world, the type of surface and its variation with optical irradiation is a key to the
transducer operation. Normally, changing the reflectivity of a surface will affect the radiation pressure
on the surface but not the energy density of the real photons. However, in the Casimir force case, Pinto
explains, “…the normalized energy density of the radiation field of virtual photons is drastically affected
by the dielectric properties of all media involved via the source-free Maxwell equations.”201
Specifically, Pinto discovered that the absolute value of the vacuum energy can change “just by
causing energy to flow from a location to another inside the volume V.”202 This finding predicts a major
breakthrough in utilization of a quantum principle to create a transducer of vacuum energy. Some
concerns are usually raised, as mentioned previously, with whether the vacuum energy is conserved. In
quantum systems, if the parameters (boundary conditions) are held constant, the Casimir force is
strictly conservative in the classical sense, according to Pinto. “When they are changed, however,
it is possible to identify closed paths along which the total work done by this force does not vanish.”203
To conclude the energy production analysis, it is noted by Pinto that 10,000 cycles per second
are taken as a performance limit. Taking the lower estimate of 100 erg/cm2 per cycle, power or
“wattage” is calculated to be about 1 kW/m2 which is on par with photovoltaic energy production.
However, on the scale of interest, where s in Figure 31 is always less than 1 μm, the single cantilever
transducer is expected to produce about 0.5 nW and establish a millivolt across a kilohm load, which is
still fairly robust for such a tiny machine.204
The basis of the dielectric formula starts with Pinto’s analysis that the Drude model of electrical
conductivity is dependent on the mean electron energy <E> (less than hf) and estimated to be in the
range of submillimeter wavelengths. The Drude model, though classical in nature, is often used for
comparison purposes in Casimir calculations.205 The detailed analysis by Pinto shows that carrier
concentrations and resistivity contribute to the estimate of the total dielectric permittivity function value,
which is frequency dependent. The frequency dependence is of increasing concern for investigations
into the Casimir effects on dielectrics.206
Figure 32 – Microlaser on a pedestal (computer simulation)
Analyzing the invention for
engineering considerations, it is clear
that some of the nanotechnology
necessary for fabrication of the
invention have only become available
very
recently.
The
one-atom
microlaser, invented in 1994, should
be a key component for this invention
since about ten photons are emitted
per atom.207 However, it has been
found that new phenomena, (1) the
virtual-photon tunnel effect and (2) the
virtual-photon quantum noise, both
have an adverse effect on the
preparation of a pure photon-number
state inside a cavity, which may
impede the performance of the
microlaser if placed inside a cavity.208
Pinto concurs that such a low
emission rate is necessary since the
lasing must take place “as a
47
succession of very small changes” 209
Another suggested improvement to the original invention could involve a femtosecond or
attosecond pulse from a disk-shaped semiconductor microlaser (such as those developed by Bell
Laboratories). The microlaser could be used in close proximity to the cantilever assembly. Such
microlaser structures, called “microdisk lasers” measuring 2 microns across and 100 nm thick, have
been shown to produce coherent light radially (see Figure 32). A proper choice of laser frequency
would be to tune it to the impurity ionization energy of the semiconductor cantilever. In this example,
the size would be approximately correct for the micron-sized Casimir cavity.
Pinto chooses to neglect any temperature effects on the dielectric permittivity.210 However, since
then, the effect of finite temperature has been found to be intimately related to the cavity edge choices
that can cause the Casimir energy to be positive or negative.211 Therefore, the contribution of
temperature variance and optimization of the operating temperature seems to have become a
parameter that should not be ignored. Also supporting this view is the evidence that the dielectric
permittivity has been found to depend on the derivative of the dielectric permittivity with respect to
temperature.212
Cavity QED Controls Vacuum Fluctuations
It is known from the basic physics of “cavity QED” that just the presence of the walls of a cavity
will cause any atoms within it to react differently. For example, “the spontaneous emission rate at
wavelength should be completely suppressed if the transition dipole moment is parallel to the mirror
plates” where the walls of the cavity are reflecting conductors.213 In other words, “a confined antenna
cannot broadcast at long wavelengths. An excited atom in a small cavity is precisely such an antenna,
albeit a microscopic one. If the cavity is small enough, the atom will be unable to radiate because the
wavelength of the oscillating field it would ‘like’ to produce cannot fit within the boundaries. As long as
the atom cannot emit a photon, it must remain in the same energy level; the excited state acquires an
infinite lifetime...[because] there are no vacuum fluctuations to stimulate its emission by oscillating in
phase with it.”214 Such effects are noticed for cavities on the order of hundreds of microns and smaller,
precisely the range of Pinto’s cavity. Therefore, it can be expected that carefully choosing the
fundamental resonant frequency of the cavity will provoke the emission of photons so that the
dielectric effect on the walls may be enhanced with less input of energy.
Furthermore, the most important Casimir force research relating to Pinto’s invention may be the
analysis of a vibrating cavity. If the membrane oscillation frequency is chosen, for example, to be close
to a multiple frequency (harmonic) of the fundamental unperturbed field mode of the cavity, resonant
photon generation will also provoked. Such resonant photon generation in a vibrating cavity like Pinto’s
has been studied in the literature.215, 216
Another aspect of the Pinto experiment apparently not discussed in his article is the relative
concentration of gas molecules in the vacuum energy transducer of Figure 30. Though a complete
evacuation of air would be preferable, especially when compression of the membrane could be
impeded by increasing gas pressures, it is naturally expected that too many gas molecules will still
remain airborne even with a high vacuum, such as 10-10 to 10-12 Torr. Therefore, using another
characteristic of cavity QED may be recommended. First of all, the selection of the gas is important, so
that the atomic transition frequency matches the cavity resonant frequency very closely. Once this is
achieved, it would be recommended, from an engineering point of view, to optimize the design of the
size of the cavity transducer so that the atomic transition has a slightly higher frequency than the
resonant frequency of the cavity. This could easily occur with the resonant wavelength slightly longer
than the resonant transition wavelength of the gas in question. In that way, the gas molecules will be
repulsed from entering the cavity, thus creating a lower gas pressure inside. Logically, this would
be accomplished with the cavity transducer in the maximum SA position in Figure 30. It would thereby
add to the compression force of the movable membrane. As the membrane reaches its lowest position
in the engine cycle with minimum SA position, cavity QED dictates that since the atomic transition
frequency will then be lower than the resonant frequency of the cavity, the force will be attractive,
48
pulling gas molecules toward the cavity
and increasing the pressure. This
condition may be accomplished as
well, since the shorter wavelength of
the smaller cavity size will now be less
than the longer wavelength of the
atomic transition wavelength of the
gas. Such a condition, with extra gas
Fig. 33 Squeezed n = 0 cavity state
molecules in the cavity, will assist in
pushing the membrane upwards
again.217 Such detailed planning with
gases and cavity dimensions should
create a situation where the ZPF is
supplying a larger percentage of the
energy output, with a minimum of
nanolaser input energy. If so, the Pinto
vacuum energy generator would offer
an unparalleled miniature electricity
source that could fill a wide range of nanotechnology needs and microelectronic needs.
Spatial Squeezing of the Vacuum
The analysis of Pinto’s invention is analogous to spatial squeezing of the initial states to
decrease the energy density on one side of a surface, below its vacuum value, in order to increase the
Casimir force. For an oscillating boundary like Pinto’s, this can also create a correlated excitation of
frequency modes into squeezed states and “sub-Casimir regions” where the vacuum develops
structure. “Pressing zero-point energy out of a spatial region can be used to temporarily
increase the Casimir force.”218 This spatial squeezing technique is gaining increasing acceptance in
the physics literature as a method for bending quantum rules
while gaining a short-term benefit, such as modulating the
quantum fluctuations of atomic displacements below the zeropoint quantum noise level of coherent phonon (vibrational)
states, based on phonon-phonon interactions.219
The squeezing technique involves minimizing the
expectation value of the energy in a prescribed region, such as a
cavity. “In general, a squeezed state is obtained from an
eigenstate of the annihilation operator…by applying to it the
unitary squeezing (or dilation) operator.”220 Ideally, “it seems
promising to generate squeezed modes inside a cavity by an
instant change of length of the cavity.”221 The implied infinite
speed or frequency for a movable membrane would not be
achievable however. If it were approachable, the squeezing
would cause a modification of the Casimir force so that it could
become a time dependent oscillation from a maximum to
minimum force. Pursuing resonance measurements may turn out
to be the most realistic experimental approach in order to exploit
the periodic variation in the Casimir force by squeezing.
In Figure 33, the effect of squeezing can be seen in the
fundamental cavity mode n = 0 where the emission of photons is
almost double that allowed by the Planck radiation law Equation
(9), where there are quantized field modes. Hu found that the
Fig. 34 Vacuum fluctuations focus
49
other field modes go to a mixed quantum state due to the intermode interaction caused by the classical
Doppler effect from the moving mirrors. The theory also predicts that the significant features of the
nonstationary Casimir effect are not sensitive to temperature.222
Focusing Vacuum Fluctuations
Another development that may directly affect transduction possibilities of ZPE is the theoretical
prediction of focusing vacuum fluctuations. Utilizing a parabolic mirror designed to be about 1 micron in
size (labeled ‘a’ in Figure 33), with a plasma frequency in the range of 0.1 micron for most metals, Ford
predicts that it may be possible to deflect atoms with room temperatures of 300K, levitate them in a
gravitational field, and trap them within a few microns of the focus F.223 A positive energy density
results in an attractive force. Depending upon the parameters, it may alternatively result in a
repulsive Van der Waals force at the focus with a region of negative energy density. This type of
trapping would require no externally applied electromagnetic fields or photons. The enhanced vacuum
fluctuations responsible for these effects are found to arise from an interference term between different
reflected rays. The interesting conundrum is the suggestion that parabolic mirrors can focus something
even in the absence of incoming light, but vacuum fluctuations are often treated as evanescent
electromagnetic fields. The manifestation of the focusing phenomenon is the growth in the energy
density and the mean squared electric field near the focus.224
Focusing vacuum fluctuations in many ways resembles “amplified spontaneous emission” (ASE)
which occurs in a gain medium, where the buildup of intensity depends upon the quantum noise
associated with the vacuum field.225
Stress Enhances Casimir Deflection
An interesting Casimir force effect, seen more and more frequently in nano-electromechanical
Figure 35 - NEMS
cantilever bridge
deflection caused by
the Casimir force
system (NEMS), is illustrated in Figure 35. Shown is a membrane or cantilever of thickness h that
covers a well of width l and height a, which is deflected in the y direction, by an amount of distance
W(x) depending upon the position with respect to x.226 The equation describing the deflection of any
point on the membrane is:
D
∂ 4 W (x )
=F
∂x 4
(31)
D = Eh3/(12-12p2) where E is the elastic modulus, h is the thickness (see Figure 35) of the membrane,
and p is the Poisson ratio. The Poisson ratio is the ratio of the transverse contracting strain to the
elongation strain.227 The Casimir force F in Equation (31), due to the proximity to the bottom plate, is an
inhomogeneous force in this situation, varying from point to point along x as228
F=−
π 2 hc
210 (a − W(x ))
4
(32)
50
where h, W(x) and a are defined above.
Equations (31) and (32) are then equated to produce a quartic equation dependent on W(x)
where the residual applied stress/strain σ can be added as a modifier. Solving for W(x) under
conditions of strain (stretching) yields a tendency toward a stationary wave pattern characteristic of
buckling, without any appreciable change in the center deflection. Solving for W(x) under conditions of
stress (compression) reveals that “compressive residual stress enhances the deflection of the bridge
and reduces its [buckling] behaviour.”229 The amount of enhancement at the center is W(0) = 0.0074a
or almost 1%. However, since the Casimir force in Equation (32) increases by the fourth power of the
distance (a – W(x)), it is also regarded as a positive feedback system, with a tendency of increasing
any deflection in a direction toward structural failure.
Casimir Force Geometry Design
Since the Casimir force is such an integral part of the experimental energy manifestations of the
ZPF as well as the Chapter 4 analysis, it is worthwhile to review some of its important characteristics.
First of all, the attractive Casimir force between two uniform, flat metal plates which are perfectly
conducting (and therefore, a reflective surface) is230
F =
– π2 hc / 240 d4
(33)
where d is the spacing between the plates. Milonni points out that besides the usual vacuum
fluctuations approach, one can also treat the virtual photons of the vacuum as “carriers of linear
momentum.” This perspective yields a mathematical proof that the Casimir force can also be classically
analyzed as a physical difference of radiation pressure on the two sides of each plate.231 In Equation
(33), if d = 1 micron, F will turn out to equal about 10-3 N/m2.
In comparison, the Coulomb force for charged plates, such as with Forward’s charge foliated
conductors of Figure 8, is found to be
FCoul
=
V2 / 8πd2
.
(34)
Thus, with a potential difference of only V = 17 mV at d = 1 μm, the Casimir force equals the Coulomb
force.232 This is also the operating principle behind Pinto’s cavity transducer of Figure 30, as the
Figure 36
Constant + / 0 / –
Casimir energy
curves for various
rectangular metal
microboxes
Casimir force is varied cyclically.
In Figure 36, a comprehensive “designer’s toolkit approach” by Maclay is made for an
arbitrarily-sized box made of perfectly conducting surfaces. As the dimensions of the box deviate
from a cubic design (1 x 1 x 1) the Casimir forces change as well.
51
Figure 37
Dotted P1 is the
pressure on the
1 x C face,
which varies
between + and
- pressure; P3
is the pressure
on 1 x 1 face
(small dots);
E / V is the
energy density
(dashed line); E
is Casimir
energy for the
metal box (solid
line)
A maximum positive energy density (dark area near the origin) signifies a positive Casimir force or
outward pressure. Effectively, positive energy density produces a repulsive Casimir force. The
dimensions of 1 x 1 x 1.7 signify the transition zone known as “zero energy density.” Any further
increase in size results in a negative or attractive Casimir force. It is readily apparent from these
calculations that a similar system, with a movable membrane like Pinto’s Figure 30, offers a restoring
force for either deviation from zero, as if the cavity held a compressible fluid.233
In Figure 37 is another vacuum engineering toolkit graph, the Casimir forces for a
perfectly conducting 1 x 1 x C rectangular box, expanding from C = 1 to an elongated size. Again,
as in Figure 36, it can be seen that as C = 1.7 the Casimir pressure P1 crosses the zero energy line. To
help distinguish the Casimir energy density E / V and Casimir energy E lines from the rest, it is noted
that these two lines cross zero at the same point C = 3.5, while the Casimir pressure P3 line stays
constant past C = 1. The E / V, E, and P3 lines are all negative when C < 1 showing the dominance of
d4 in the denominator of Equation (33), when two surfaces approach 1 micron or less.
The discovery by Maclay of a particular box dimension (1 x 1 x 1.7), that sits in the middle of
attractive and repulsive Casimir forces, presents a possible scenario for vacuum energy extraction.
“This interesting motion suggests that we may be organizing the random fluctuation of the EM field in
such a way that changes in pressure directly result, which could lead to work being done. One
interesting question is can we design a cavity that will just oscillate by itself in a vacuum. One approach
to this would require a set of cavity dimensions such that the force on a particular side is zero, but if the
side is moved inward, a restoring force would be created that would tend to push it outward, and vice
versa. Hence a condition for oscillation would be obtained. Ideally, one would try to choose a
mechanical resonance condition that would match the vacuum force resonance frequency. More
complex patterns of oscillation might be possible. The cavity resonator might be used to convert
vacuum fluctuation energy into kinetic energy or thermal energy. More calculations of forces within
cavities are needed to determine if this is possible, what would be a suitable geometry and how the
energy balance would be obtained.”234 Maclay concedes however, that upon analyzing Forward’s
charged parking ramp of Figure 8, with like charges supplying the restorative force to the Casimir
attractive force, that no net work would be done for any given oscillation cycle.
When dielectrics are considered, the analysis becomes more involved. “Calculations of Casimir
forces for situations more complicated than two parallel plates are notoriously difficult, and one has little
52
intuition even as to whether the force should be attractive or repulsive for any given geometry.”235 With
a dielectric set of parallel plates, the characteristics of dispersive (phase velocity is a function of
frequency) or non-dispersive (all frequencies equally transmitted or reflected) dielectrics enters into the
equation. For example, a classic example is two dispersive dielectric parallel plates that have a Casimir
energy which depends only on the distance between the plates and the dispersion of the dielectrics.236
Various geometries of rectangular cavities can also be studied using the principle of virtual work
where E = - ∫ F dx. With the Casimir vacuum energy E for a dielectric ball of radius a, for example, the
Casimir force per unit area is,
F =−
1 ∂E
4πa 2 ∂ a
(35)
For a dilute, dispersive dielectric ball for example, the Casimir surface force is found to be attractive
with inward pressure.237 A system of two dielectric spheres with general permittivities and some chosen
values of the refractive index n has also been evaluated for Casimir forces.238
One application for this type of Casimir force calculation lies with biological cells which are
spheres with a high dielectric constant. Figure 38 shows a B-lymphocyte which is 1 micron across
which therefore must experience and compensate for the inward Casimir pressure. “Biological
structures may also interact with the vacuum field. It seems possible that cells, and components of
cells, for example, the endoplasmic reticulum may interact with the vacuum field in
specific ways. A cell membrane, with a controllable ionic permeability, might
change shape in such a way that vacuum energy is transferred. Microtubules, in
cell cytoskeletons, may have certain specific properties with regard to the vacuum
field. Diatoms, with their ornate geometrical structures, must create interesting
vacuum field densities; one wonders if there is a function for such fields.”239 Many of
these structures that are less than one micron in size have much higher Casimir
pressures to contend with, such as ribosomes which are about 0.02 micron
Figure 38
across.240
B-lymphocyte
Other geometrical objects have also been analyzed for the resultant Casimir forces such as
hemispheres, pistons, and flat, circular disks.241 Instead of solid objects, configurations such as
spherically symmetric cavities have also been presented in the literature.242 Rectangular cavities, for
example, have also been found to have a temperature dependence and edge design variations which
can lead to the Casimir energy being positive or negative.243
Another interesting area of possible energy extraction from the Casimir effect is in astronomical
bodies such as stars. The Casimir effect has been proposed as a source of cosmic energy. In such
cosmological objects as white dwarfs, neutron stars, and quasars, the volume effect of the Casimir
force is theoretically sufficient to explain the huge output of quasars for example. A calculation of the
shift in energy density of the ZPF due to the presence of an ideal conductor in a volume V of space
relative to the case with an absence of the volume is the mean value of the stress-energy tensor of
QED inside volume V. A conductive material will be conductive for frequencies below the plasma
frequency ω < ωp and transparent for frequencies above the plasma frequency ω > ωp. The plasma
frequency, for nonpropagating oscillations depending only on the total number of electrons per unit
volume is, in Gaussian units, 244
ωp2
=
4π ne2 / m
.
(36)
The dielectric constant for high frequencies is also dependent on the plasma frequency (compare with
Figure 15),
ε (ω ) =
1 – ωp2 / ω2
.
(37)
53
(In dielectric media, Equation (37) applies for ω2 >> ωp2.) The shift in the vacuum energy density due to
the presence of a volume of ideal conducting material is, expressed in terms of the plasma frequency,
Δ Evac
=
– ωp4 h c / 4π2
.
(38)
With a dramatic increase in the electron density n due to gravitational compression in collapsing stars,
an energy creation is predicted that compares with 1038 J expected for a nova or 1042 J for a supernova
if the radius of the star is compressed to approximately R ≈ 107 m.245
Vibrating Cavity Photon Emission
Various cavities have been analyzed so far for the net Casimir effect. However, the case of
photon creation from the vacuum due to a non-stationary Casimir effect in a cavity with vibrating wall(s)
is unique and has interesting ramifications. Comparing with Pinto’s cavity of Figure 30, the cavity
chosen by Dodonov to create resonance photon generation also has one moving wall while the rest of
the rectangular cavity is stationary. The fundamental electromagnetic mode is ω1 = π c / Lo where Lo is
the mean distance between the walls of the cavity. The maximum value of the energy is found to be
three times the minimum value, depending on the phase. The total energy also oscillates in time and
the photon generation rate tends toward a constant value as long as any detuning is less than one.
While changes in the dielectric constant of cavity walls affect the Casimir vacuum force of
Pinto’s vibrating cavity, there are also effects from a change in the refractive index of a medium.
Hizhnyakov presents evidence for the emission of photons from such a distortion of the spectrum of
zero point quantum fluctuations. If the medium experiences a time-dependent refractive index, it has
been demonstrated that part of the energy will be emitted as real photons. An example is a dielectric
medium excited by a rectangular light pulse for about a femtosecond (10-15 seconds). The spectral
density of the photon energy is shown to depend only upon the rate of change of the refractive index
over time, which is unusual. While Hawking and Unruh radiation effects are mixed thermal states, this
refractive index derivative effect is said by Hizhnyakov to be a pure state equally related to the ZPF as
a non-linear quantum optical effect. In terms of energy flow, a picojoule (10-9 J) laser pulse lasting for a
femtosecond produces about ten megawatts (10 MW/cm2) of power input and the input pulse has about
10-5 cm2 cross sectional area which gives about a 100 W power input. The output intensity, estimated
to be about a picowatt, is calculated to be the sum of two pulses created from the leading and trailing
edges of the input refractive index change.246
The Unruh radiation referred to above is actually called the Unruh-Davies Effect which refers
to a phenomenon related to uniform acceleration. In a scalar field such as the ZPE vacuum, “the effect
of acceleration is to ‘promote’ zero-point quantum field fluctuations to the level of thermal
fluctuations.”247 Milonni points out that it took a half a century after the birth of quantum theory for the
thermal effect of uniform acceleration to be discovered. The effective temperature that would be
measured by an accelerated detector in a vacuum is
TU =
ha
2π kc
(38)
which leads to the interpretation that thermal radiation is very similar to vacuum fluctuation radiation. In
Equation (38), k is the wave number (ω/c) and a is the acceleration. Both vacuum probability
distribution functions and thermal distributions exhibit a Gaussian probability distribution since the
vacuum distribution is the T Æ 0 limit of the thermal distribution.248
Looking at Hawking radiation, which is emitted from a black hole, it is based on the premise that
pair production from the vacuum can occur anywhere, even at the event horizon of a black hole. The
treatment is related to a mathematical manipulation called Wick rotation, where the metric is rotated
into the complex plane with time t Æ - i t, so that the temperature is inversely equal to the period.
54
Solving for the region just outside the event horizon r > 2GM, where G is the gravitational constant, the
Hawking temperature is found to be
TH =
hc 3
8π GM
(39)
where M is the mass of the black hole.249 Since Planck’s constant is included in Equation (39), Zee
notes that Hawking radiation is indeed a quantum effect. The similarities between Equations (38) and
(39) are referred to by Hizhnyakov (endnote 245).
Fluid Dynamics of the Quantum Vacuum
In the analysis of Figure 37, it was mentioned that the Casimir force within cavities of Pinto and
Maclay, possessing one movable wall, behave like a compressible fluid since a restoring force is
present for any deviation from the zero-force position. It turns out that more exact analogies to fluids
are possible for the quantum vacuum. A hydrodynamic model of a fluid with irregular fluctuations has
been proposed by Bohm and Vigier for the vacuum, which also satisfies Einstein’s desire for a causal
interpretation of quantum mechanics.250 Their work also includes a proof that the wave function
probability density P = |ψ|2 used in quantum theory approaches the standard formula for fluid density
with random fluctuations. There is also a suggestion of further work regarding how a fluid vortex
provides a very natural
Figure 39
model of the non-relativistic
Flight
wave equation of a particle
resistance
with spin.
vs. speed
utilize the
same form
equation in
air or in
space
A
computational
fluid dynamics approach to
the ZPF, with the ambitious
aim of reducing flight
resistance at superluminal
speeds has been proposed
by Froning and Roach.251 The negative
energy density region seen in Figure 37
between Casimir plates is also implicated in
spacetime warping concepts and a theoretical increase in the speed of light. Resistance to flight in air
and space have interesting parallels in this theory. In Figure 39, the aerodynamic viscous drag
resistance to increased speed is compared
to the electromagnetic zero-point vacuum
resistance
to
increased
speed,
which
is
perceived
as
Figure 40
inertia. Drawing upon the
Acoustic
and
separate works by Puthoff
electroand Haisch (cited in Chapter
magnetic
2), this approach takes their
wave
ZPE-related
gravity
and
drag or
inertia
theory
to
the
inertial
engineering
level
of
actually
experimental
simulation.
In
do use
Figure 40, the analogy is
the same
drawn between the wellequation!
known
equation for the
speed of light c = ( μoεo )-½ and the
aerodynamic gas equation for the speed of
sound c = (gRγT)-½ with compressible fluid graphics for each. The aerodynamic resistance of viscous
55
drag exerted on the substructure of a vehicle is compared to the Lorentz force exerted on the
substructure of the vehicle by the ZPF, which is also proposed to be a Casimir-like force exerted on the
exterior by unbalanced ZPE radiation pressures. The conclusion drawn from this first-order
analysis is that μo and εo can be perturbed by propagation speed and possibly vehicle inertia,
accompanied by a distortion of the zero-point vacuum.
A fundamental part of the Fronig and Roach approach to the fluid dynamic simulation of
superluminal speeds is the proposal that μo and εo can be reduced significantly by nonabelian
electromagnetic fields of SU(2) symmetry. It is proposed that EM fields of nonabelian form have the
same symmetry that underlies gravity and inertia. Their approach is particularly to use alternating
current toroids with resonant frequencies. That nonabelian gauge symmetry offers a higher order of
symmetry has been seen elsewhere in the literature. Zee, for example, notes that the square of the
vector potential A2 would normally be equal to zero in the abelian gauge, which all standard (“trivial”)
electromagnetic theory texts use. Instead, he notes that a field strength such as F = dA + A2 can be
formulated easily in the nonabelian gauge and shown to be nonzero and gauge covariant (though not
invariant). Furthermore, the nonabelian analog of the Maxwell Langrangian, called the Yang-Mills
Langrangian, includes cubic and quartic terms that describe self-interaction of nonabelian bosons
(photons), as well as a nonabelian Berry’s phase that is intimately related to the Aharonov-Bohm
phase. (The Aharonov-Bohm phase depends exclusively on the vector potential.) Even the strong
nuclear interaction is accurately described by a nonabelian gauge theory. “Pure Maxwell theory is free
and so essentially trivial. It contains a noninteracting photon. In contrast, pure Yang-Mills theory
contains self-interaction and is highly nontrivial…Fields listen to the Yang-Mills gauge bosons according
to the representation R that they belong to, and those that belong to the trivial identity representation do
not hear the call of the gauge boson.”252
According to Froning and Roach, the representation R can be changed by surrounding a
saucer-shaped spaceship with a toroidal EM field that distorts and perturbs the vacuum sufficiently to
affect its permeability and permittivity. The vacuum field perturbations are simulated by fluid field
perturbations that resulted in the same percentage
change in disturbance propagation speed within the
region of perturbation. The computational effort was
simplified by solving only the Euler equations of
fluid dynamics for wave drag. The resulting μo and
εo perturbation solutions are shown in Figure 41.
In his discussion of the 1910 Einstein-Hopf
model, Milonni describes their derivation of a
retarding force or drag on a moving dipole as a
result of its interaction with the vacuum zero-point
field, which acts to decrease its kinetic energy.
Assuming v << c, the retarding force due to motion
through the ZPF thermal field is described with a
fluid dynamics equation, F = – R v, where v is the
velocity of the dipole and R is a formula depending
upon dipole mass and ZPF spectral energy density.
Milonni also notes that due to recoil associated
with photon emission and absorption, which are
both in the same direction, the ZPF also acts to
increase the kinetic energy of a dipole.
Equilibrium is established when the increase in kinetic energy due to recoil balances the decrease in
kinetic energy due to the drag.253
Figure 41 Topology of vacuum field disturbance
It has been proposed by Rueda and Haisch,
with a contract from NASA, that the ZPF can lose
its Einstein-Hopf drag as the absolute
56
temperature approaches zero, which would leave only the accelerating recoil force left. (The
temperature of outer space is about 3K, or 3 degrees above absolute zero.) Furthermore, they propose
that the ZPF can provide a directional acceleration to monopolar particles more effectively that to
polarizable particles. They also suggest that “if valid, the mechanism should eventually provide a
means to transfer energy, back and forth, but most importantly forth, from the vacuum electromagnetic
ZPF into a suitable experimental apparatus.”254
Quantum Coherence Accesses Single Heat Bath
One of the main criticisms of energy extraction from the ZPF is that it represents a single
low-temperature bath and the second law of thermodynamics prohibits such an energy
conversion. It is well-known that Carnot showed that every heat engine has the same maximum
efficiency, determined only by the high-temperature energy source and the low-temperature entropy
sink. Specifically, it follows that no work can be extracted from a single heat bath when the high and low
temperature baths are the same.
However, a new kind of quantum heat engine (QHE) powered by a special “quantum heat
bath” has been proposed by Scully et al. which allows the extraction of work from a single
thermal reservoir. In this heat engine, radiation pressure drives the piston and is also called a “PhotoCarnot engine.” Thus, the radiation is the working fluid, which is heated by a beam of hot atoms. The
atoms in the quantum heat bath are given a small bit of quantum coherence (phase adjustment) which
becomes vanishingly small in the high-temperature limit that is essentially thermal. However, the phase
associated with the atomic coherence, provides a new control parameter that can be varied to increase
the
temperature
of
the
radiation field and to extract
work from a single heat bath.
The
second
law
of
thermodynamics
is
not
violated, according to Scully et
al., because the quantum
Carnot engine takes more
energy, with microwave input,
to
create
the
quantum
coherence
than
is
generated.255
Figure 42 Photo-Carnot heat cycle diagram. Qin is provided by hot atoms
The Photo-Carnot engine, shown in Figure 42, creates radiation pressure from a thermally
excited single-mode field that can drive a piston. Atoms flow through the engine from the Th heat bath
and keep the field at a constant temperature for the isothermal 1Æ 2 portion of the Carnot cycle (Figure
43). Upon exiting the engine, the bath atoms are cooler than when they entered and are reheated by
interactions with the blackbody at Th and "stored" in preparation for the next cycle.
Figure 43
Temperature –
entropy
diagram for
Photo-Carnot
engine where
input Th equals
the output Tc
The stimulus for the work came
from two innovations in quantum
optics: the micromaser and microlaser
(Figure 32) and lasing without
inversion (LWI). In micromasers and
microlasers, the radiation cavity
lifetime is so long that a modest beam
of excited atoms can sustain laser
oscillation. In LWI, the atoms have a
nearly degenerate pair of levels
57
making up the ground state. When the lower level pair is coherently prepared, a small excited state
population can yield lasing (without inversion). In the QHE, the "engine" is a microlaser cavity in which
one mirror is a piston driven by the radiation pressure given by
PV =
nhπc/L
(40)
where P is the radiation pressure, V is the cavity volume, n is the average number of thermal photons in
the right mode (about 103), and L is the length of the cavity.256 In Figure 43, an engine cycle diagram is
shown which is a temperature versus entropy graph for the Photo-Carnot engine, where |ρbc| ≈ 3 x 10-6
is an off-diagonal density matrix element in the extension of the quantum theory of a laser without
inversion. Figure 43 contains a closed cycle of two isothermal and two adiabatic processes (compare
with Pinto’s Figure 31). Qin is the energy absorbed during the isothermal expansion and Qout is the
energy given to the heat sink during the isothermal compression. However, instead of two states which
would render this a classical engine, the QHE has three states, which can result in quantum coherence.
“If there is a non-vanishing phase difference between the two lowest atomic states, then the atoms are
said to have quantum coherence. This can be induced by a microwave field with a frequency that
corresponds to the transition between the two lowest atomic states. Quantum coherence changes the
way the atoms interact with the cavity radiation by changing the relative strengths of emission
and absorption.257 In Figure 42, as the atoms leave the blackbody at temperature Th they pass
through a microwave cavity that causes them to become coherent with phase Φ before they enter the
optical cavity. The temperature that characterizes the radiation is TΦ which is
TΦ = Th (1 – n ε cos Φ)
(41)
where ε is the magnitude of quantum coherence, ε = 3|ρbc|. The second term in Equation (41) is also
used in the QHE efficiency equation,
ηΦ = η – ( Tc/Th ) n ε cos Φ
(42)
“Thus, depending on the value of Φ, the efficiency of the quantum Carnot engine can exceed that of the
classical engine – even when Tc = Th . It can therefore extract work from a single heat bath.”258
Inexplicably, Scully et al. fail to cite a previous work by Allahverdyan and Nieuwenhuizen
that utilizes more rigorous physics for same purpose of extraction of work from a single thermal bath in
the quantum regime with quantum coherence. The authors, perhaps, have more controversial
statements in the article regarding free energy extraction. Using the quantum Langevin equation for
quantum Brownian motion, they note that it has a Gibbs distribution only in the limit of weak damping,
thus preventing the applicability of equilibrium thermodynamics. The reason is related to quantum
entanglement and the necessary mixed state. “Our main results are rather dramatic, apparently
contradicting the second law: We show that the Clausius inequality dQ < TdS can be violated,
and that it is even possible to extract work from the bath by cyclic variations of a parameter
(“perpetuum mobile”). The physical cause for this appalling behavior will be traced back to quantum
coherence in the presence of the near-equilibrium bath.”259 It is also emphasized that the quantum
coherence is reflected in the quantum noise correlation time which exceeds the damping time 1/ Γ.
Regarding the ZPF, it is interesting that the quantum Langevin equation is a consequence
of the fluctuation-dissipation theorem of Equation (11). The authors note that part of the equation
includes the fluctuating quantum noise, which has a maximum correlation time and therefore has a long
memory (quantum coherence) at low temperature. The Brownian particle of interest also has semiclassical behavior due to its interaction with the bath, where notably, “there is a transfer of heat, even
for T = 0.”260
The possibility of extracting energy from the bath is due to the nonequilibrium state, which is
ensured by the switching energy ½ γ Γ<x2>o that is also a purely classical effect. The switching energy
depends upon γ which is the damping constant and Γ which is the cutoff frequency. Both harmonic and
anharmonic oscillation potentials are considered. The Brownian quantum particle strongly interacts with
the quantum thermal bath, described by the Fokker-Planck equations.
58
“Two formulations of the second law, namely, the Clausius inequality and the impossibility to
extract work during cyclical variations, can be apparently violated at low temperatures. One could thus
speak of a ‘perpetuum mobile of the second kind.’ We should mention, however, that the number of
cycles can be large, but not arbitrarily large. As a result, the total amount of extractable work is modest.
In any case, the system energy can never be less than its ground state energy…We call them apparent
violations, since, the standard requirements for a thermal bath not being fulfilled, thermodynamics just
does not apply. Let us stress that also in the classical regime the harmonic oscillator bath is not in full
equilibrium, but there noise and damping have the same time scale 1/ Γ, allowing the Gibbs distribution
to save the day and thermodynamics to apply. Our results make it clear that the characterization of the
heat bath should be given with care. If it thermalizes on the observation time, standard thermodynamics
always applies. Otherwise, thermodynamics need not have a say…The finding that work can be
extracted from quantum baths may have a wide scope of applications such as cooling."261
In a physics commentary, Linke defends the second law by insisting that the work done by the
Scully et al. piston (in Figure 42) is less than the work required to establish quantum coherence. Linke
clarifies the Photo-Carnot process by stating, “When the phase difference is adjusted to the value π,
destructive interference reduces the likelihood of photon
absorption, whereas emission from the upper level is not
affected. This deviation from detailed balance between
photon absorption and emission increases the photon
temperature. The resulting temperature difference between
photon gas and heat bath allows the photon Carnot engine
to produce work in the absence of a hot bath.”262
Thermodynamic Brownian Motors
There is still another aspect of the ZPF that
presents the possibility of energy extraction, which are
nonequilibrium fluctuations — a different representation of
the single heat bath. Biasing the Brownian motion of a
particle in an anisotropic medium without thermal gradients,
the force of gravity, or a macroscopic electric field is a way
that usable work is theoretically generated from
nonequilibrium fluctuations, such as those generated
externally or by a chemical reaction far from equilibrium.
Fluctuation-driven transport is one mechanism by which
chemical energy can directly drive the motion of particles
and macromolecules and may find application in a wide
variety of fields, including the design of molecular motors
called “Brownian motors” and pumps.263
Figure 44 - Fluctuation-driven transport
(B) velocity vs. maximum force;
(C) velocity vs. thermal noise
Brownian motion, the random collisions with solvent
molecules by a particle in a liquid, has been studied
historically by Einstein as well as by Langevin. Langevin’s
equation, as noted in the previous section, suggested that
the forces on the particle due to the solvent can be split into
two components: (1) a fluctuating force that changes
direction and magnitude frequently compared to any other
time scale of the system and averages to zero over time,
and (2) a viscous drag force that always slows the
motions induced by the fluctuation term. Related to the
fluctuation-dissipation theorem of Equation (11), the
amplitude of the fluctuating force is governed by the
viscosity of the solution and by temperature, so the
fluctuation is often termed thermal noise. Even in an
59
anisotropic medium, the fluctuations are symmetric as required by the second law of thermodynamics,
as are the dissipative drag force. Therefore, when all components of fluctuation-driven system are
treated consistently, net motion is not achieved if it is an isothermal system, despite the anisotropy of a
ratchet's teeth. However, a thermal gradient in synergy with Brownian motion can cause directed
motion of a ratchet and can be used to do work but these are hard to maintain in microscopic and
molecular systems. Recent work has focused, instead, on the possibility of an energy source other than
a thermal gradient to power a microscopic motor.264
Astumian proposes a fluctuating electrical potential that causes the uphill transport of a particle.
A fluctuating potential energy profile is provided with an anisotropic sawtooth function Usaw and
periodically spaced wells with no net macroscopic force. When the potential is off, the energy profile is
flat with a uniform force everywhere. When the potential is turned on again, the particle is trapped in
one of the wells. The result is resolved into two components: the downhill drift and the diffusive
spreading of the probability distribution. For intermediate times, it is more likely for a particle to be
trapped in one of the uphill wells if the potential were turned back on, than between the first and second
well. Thus, turning the potential on and off cyclically can cause motion to the right and uphill against
gravity despite the net force to the left. The theory has been successfully tested with colloidal particles
with anisotropic electrodes turned on and off, as well as with an optical trap modulated to create a
sawtooth potential.
Figure 44 shows the basic mechanism by which a fluctuating or oscillating force can cause
directed motion along a ratchet potential Usaw and also some statistics of an example. The presence of
thermal noise allows a subthreshold fluctuating force to cause flow. The force is modulated between +
Fmax where the average velocity <v> is calculated as a function of Fmax where the dashed lines (B)
indicate the threshold forces. Another example is shown (C) where average velocity is plotted as a
function of the thermal noise strength kBT, where kB is Boltzmann’s constant and T is the absolute
temperature and Fmax = 0.4 pN. The (C) graph shows that, up to a point, increasing the noise can
actually increase the flow induced by a fluctuating force. However, the (B) graph shows that for forces
near the optimum (about 1.5 pN in this example), the velocity decreases with increasing noise.265
A more general approach is suggested for analyzing fluctuation-driven transport using the
diffusion equation with a probability density given by the Boltzmann distribution P(x) ≈ exp(-U/ kBT).
Since modulating the potential certainly requires work, Astumian believes there is no question of
these devices being perpetual motion machines. The surprising aspect is that flow is induced without a
Figure 45 Net current for quantum ratchet. Solid lines, T= 0.4K. Dotted lines, T= 4K. Inset
SEM shows four repeating ratchet cells. Temperature-dependent current reversal at a, b, c.
60
macroscopic force. All of the forces involved are local and act on a length scale of the order of a single
period of the potential. Yet the motion persists indefinitely, for many periods. However, the direction of
the flow depends upon how the modulation is applied. Such devices are indicated to be consistent with
the behavior of molecules.
In a dramatic confirmation of the Astumian theory, two subsequent experiments were performed
by Linke et al. which applied an electron ratchet in a tunneling regime with a “rocking-induced current
(tunneling through and excitation over the ratchet’s energy barrier) flow in opposite directions. Thus the
net current direction depends on the electron energy distribution at a given temperature.”266 The
practical aspect of this experimental approach is that a square wave source-drain voltage is applied
with the time-averaged electric field being zero, similar to AC electricity, and yet the output net current
is DC, similar to a rectifier.
Figure 45A shows in the inset the asymmetrical darker regions which are etched trenches that
laterally confine a two-dimensional sheet of electrons located parallel to the surface of a GaAs/AlGaAs
heterostructure. Figure 45B inset compares the barrier height Vo with the electron energy |eU| < 1
meV. The trench's periodic variation in width induces a corresponding variation in electron confinement
energy that creates asymmetric energy barriers at each constriction. When the square wave sourcedrain bias voltage is applied, the resulting current I is plotted for two devices R10 and R1. Because of
the geometric asymmetry, the electric field along the channel produced by the voltage deforms the
barriers in a way that depends on the polarity of the voltage, trapping the electrons in one of the side
gates along the x direction. The quantum ratchet is thus established by confining electrons to an
asymmetric conducting channel of a width comparable to the electron wavelength. The experiment
demonstrates importance of resonant design and fulfills the theoretical prediction that a fluctuating
voltage is sufficient to cause a unidirectional current.
The detailed theoretical model of the tunneling ratchet is shown in Figure 46. The difference ∆t
between
the
transmission
functions for the barrier potential
Vo in Figure 45B inset is graphed
(solid curve) for a rocking
voltage Uo = 0.5 mV. The bottom
of Figure 46 shows visually the
approximate equality of the
barrier height Vo and the Fermi
energy μF of 12 meV. The “thin”
curves
are
identified
by
temperature and are graphed
against the energy range ∆f of
the right hand ordinate axis. The
Figure 46 top inset shows the
dramatic difference between the
solid curve quantum mechanical
behavior (qm) and the classical
(cl) transmission function versus
electron energy ε for Uo = 0. The
classical step function occurs at
ε = Vo which is the Fermi energy
μF. Note the Figure 46 lower
inset which summarizes the net
current I in picoamperes versus
temperature,
for
rocking
Figure 46 Theoretical model of the quantum electron ratchet
voltages Uo = 0.7 mV (dashed
curve), 0.5 mV (solid curve), and
61
0.3 mV (dotted curve). All temperatures in this experiment were within a few degrees of absolute zero.
Transient Fluctuation Theorem
Another development in the thermodynamics of microscopic systems has recently redefined the
concept of work. In a system connected to a single heat bath, uncertainties on the order of kBT will arise
from the Boltzmann distribution of energies in the initial and final states, as well as from energy
exchange with the heat bath as the system goes from initial to final energy states. Because of the
thermal fluctuations or energy uncertainties, it has now been proven by theory and experiment, that the
work cannot be uniquely specified, even if the path is known. When the system is microscopic, the
fluctuations are significant and a transient fluctuation theorem has evolved to account for the behavior
which takes the form,
P(W) / P(-W)
=
eW
(43)
where W is the work divided by kBT and P(W) is the probability of performing positive work over an
interval of time, while P(-W) is the probability of performing negative work over the same period of time
.267 It needs to be clarified that in these
microscopic systems, work is measured as it is
delivered to a vessel but half the time the
system goes in reverse, apparently violating
the law of entropy. In Figure 47, a Poisson
distribution is shown of an optical trap
interacting with an experimental vessel having
micron-sized beads. Though the trap exerted a
restoring force, as for the spring in Figure 2, the
experimentally-determined values measured
for the bead position in the integrated
fluctuation theorem showed a nonzero
probability for negative work, for up to two
seconds.
“Imagine, as is often the case, that after
a certain time, the bead has a higher energy
than it had initially. Then, if the work done by the trap on the vessel (bead plus bath) is negative, energy
has been delivered to both the bead and the optical trap interacting with the vessel. That energy came
from the water bath—just the sort of energy transfer prohibited by the second law in the
thermodynamic limit of infinitely large systems: Heat has been converted to work with 100%
efficiency.”268
Figure 47 Positive (solid), negative (dots) work over time
Figure 48 Nonequilibrium Metropolis Monte Carlo simulation
The generalized transient fluctuation
theorem has various forms depending upon
the application. For example, the probability
ratio in Equation (43) can instead relate to
entropy production w for forward and reverse
time, where microscopic reversibility is an
essential requirement. The theorem finds its
greatest utility in the application to single heat
baths and systems driven by a stochastic
(random), microscopically-reversible (timesymmetric), periodic process. Then, the only
Gaussian distribution that satisfies the
fluctuation theorem has a variance that is
twice the mean 2<w> = <(w-<w>)2>, which is
a version of the standard fluctuationdissipation relation of Equation (11).269 It is
62
noted that entropy production, which is irreversible dissipation, is directly related to the fluctuations.
An example of a systematic application of the fluctuation theorem, reminiscent of the quantum
ratchet concept seen previously, is a Metropolis Monte Carlo simulation by Crooks, illustrated in
Figure 48. A single particle occupies a finite number of positions in a one-dimensional box with periodic
boundaries and coupled to a heat bath of T = 5. The energy surface E(x) is outlined by a series of
dashed (–) lines. The equilibrium distribution to be expected from such a potential well is shown as a
symmetric hill with open circles Ο since the particle is free to move with equal probability to the right,
left, or to stay put. However, every eight time intervals, the energy surface moves to the right by one
position.
In this way, the system is driven away from equilibrium and settles into a time-symmetric,
nonequilibrium steady state distribution shown by black dots ●, skewed to the left. The master equation
for this system can be solved exactly to compare with the theory.270
Power Conversion of Thermal Fluctuations
While many recent scientific advances in the treatment of nonequilibrium energy fluctuations
have been reviewed so far, there are also developments in the area of nonlinear equilibrium thermal
fluctuations. Based on the Nyquist theorem (another name for the fluctuation-dissipation theorem) and
van Kampen’s work on nonlinear thermal fluctuations in diodes, Yater’s pioneering work involves the
use of microscopic diodes in a simple circuit, whose “results gave higher conversion efficiencies than
the Carnot cycle for certain limiting cases as these model sizes decreased."271 While the use of two
heat baths suggests a thermionic energy source, his detailed analysis makes it clear that the energy
fluctuation conversion is added to a heat pump thermal conversion cycle, for example, yielding a factor
of 10 improvement.272
Yater offers a simplified master equation for the output rectified current from an independent
particle model,
I (N) ≈
exp [ (β – α)(N – ½ ) – (βm + αn)] – 1
(44)
2
where β = q / kBTcC, N = the number of excess electrons in the total circuit capacitance C, and α = q2 /
kBTrC. The designation of n and m are related: n = CcV/q and m = CrV/q where C = Cc + Cr.273 The
forward and reverse diode currents in Figure 49 also combine in textbook fashion to produce the total
current of Equation (44):
I (N) ≈
I1a I2b – I2a I1b
(45)
A Schottky barrier diode, for example,
at the liquid Helium temperature of Tc = 1K can
be used for the cold bath Tr in Figure 49. For
such a diode the nonlinearity factor is β = 1.16
x 104 e/C where C is the capacitance of the
diode (C ~ 10-16F) and e is the charge on the
electron. A Schottky diode is also known to be
formed between a semiconductor and a metal,
with nonlinear rectifying characteristics and fast
switching speeds.274
Yater notes that “for the long range
design goals, sub-micron circuit sizes are
required if all the high power goals of
megawatts per square meter are to be achieved…The results of an analysis of the independent particle
model for both classical and quantum effect, show that the reversible thermoelectric converter with
power conversion of energy fluctuations has the potential of achieving the maximum efficiency of the
Carnot cycle. The potential applications of this device can be seen to be universal.”275 His patent
Figure 49 Energy fluctuation conversion circuit
63
#4,004,210 clarifies that the electric energy fluctuations are transmitted from the higher temperature
diode to the lower temperature diode while the heat transfer is in reverse, which is unusual.
Upon reviewing the literature, Yater summarizes his findings: “The relation of the second law of
thermodynamics to the power conversion of fluctuation energy has been of recurring interest and study.
The results of these studies have ranged from the conclusion that conversion of fluctuation energy is
prohibited by the second law to the conclusion that the conversion of fluctuation energy is not
limited by the second law of thermodynamics.”276
Rectifying Thermal Noise with Ratchets
Particles that move aperiodically due to thermal or external noise, in the presence of
asymmetric periodic potentials, have also been called “stochastic ratchets.” These systems have the
intriguing ability to rectify symmetric correlated noise and thus have the ability to produce a net
electrical current. As a consequence of the fluctuation-dissipation theorem, the ratchet does not drift (as
in the Metropolis Monte Carlo simulation of Figure 48) if it is in interaction only with a thermal bath. An
external forcing must be used to produce the drift, according to the researchers, Ibarra-Bracamontes
et al.277
By describing the ratchet system in the Brownian particle regime with the Langevin equation
(like Allahverdyan and Nieuwenhuizen), thermal noise is considered to have finite correlation times.
This treatment yields a prediction of current production due to a time-dependent external force. In this
case, the external force is either sinusoidal or stochastic. The generalized Langevin equation is an
embellishment of Newton’s equation, F = ma, describing a particle of mass m moving in an asymmetric
periodic potential V(x) that forms the ratchet,
m d2x/dt2 = – ∫ d(t’) Γ(t – t’) dx(t’)/dt’ – dV(x)/dx + f(t) + Fext(t) .
(46)
Γ(t) is the dissipation kernel, which in this case has memory and correlated with friction. The term, f(t),
is the stochastic fluctuating thermal force exerted by the bath which has a usual stochastic property
of being Gaussian with zero
mean. By a numerical solution,
Equation (49) does not show a
net current in the absence of
external forces (if Fext(t) = 0).
However,
adding
a
timesymmetric external force in
general is a necessary and
sufficient
condition
for
the
Langevin equation to yield a
current flow in one direction.
Rather than argue in favor
of nonequilibrium fluctuations
being present with a symmetric
correlated force, the emphasis is
made in this case in favor of an
external origin for the force. In
accordance with the second law
of thermodynamics, the assertion
is also made here that "one
cannot extract a current from a thermal bath, whether white or colored.”278 Colored noise is where
some frequencies dominate the noise spectrum and is also referred to as “pink” noise. The average
Figure 50 Net current as particle position x versus time t for five
different ratcheting external force Fo values - Ibarra-Bracamontes.
64
position of the electron <x> is shown in Figure 50 for five different external force amplitudes versus
time. The solution demonstrates the Metropolis Monte Carlo simulation, with a different ratchet design
than Figure 48. However, it is not clear that Ibarra-Bracamontes et al. have succeeded in proving their
controversial claim that “any external forcing may be used to produce the drift” but the rectification of
thermal noise due to an asymmetric external potential has been demonstrated.
Ferrofluid Thermal RecifierTorque Engine
An experimental demonstration of rectifying random thermal fluctuations involves ferrofluids,
which are colloidal suspensions of nanoparticle ferromagnetic grains (~10 nm). In this case, the
external potential is an anharmonic oscillating magnetic field { f(t)=cos(ωt)+Asin(2ωt+β) } created by
Hemholtz coils Hy at a distance from the ferrofluid. It is regarded as a rotating magnetic field since there
is a static magnetic field Hx at right angles to the oscillating field which sums to create rotation and
angular momentum (Figure 51). The angular momentum of electromagnetic fields is a principle of
classical physics. Without thermal fluctuations, relaxation dynamics tend to cause the particles to align
with the field in the x-y plane and no average rotation nor torque is created. In the presence of
thermal fluctuations however, stochastic transitions occur due to the magnetic field asymmetry,
yielding slightly different probabilities for the magnetic orientational motion of the ferromagnetic grains,
as discovered by Engel et al.279
As with the Photo-Carnot engine, the Fokker-Planck equation is also used in this case for a
quantitative solution of the induced torque effect in the ferrofluid. Solving the equation by expansion in
spherical harmonics, the transitions between
deterministic solutions become possible. “The
spatial asymmetry and temporal anharmonicity
of the potential results in slightly different rates
for noise-induced increments and decrements of
[phase] φ, respectively. As a result, a noisedriven rotation of the particles arises.”280 There
is viscous coupling between the ferromagnetic
grains and the carrier liquid so that the
individual torques add to create a macroscopic
torque per fluid volume, N = μo M x H. However,
Engel et al. admit that the time-averaged Nz is
much smaller than the typical values of the timeindependent Nz calculated from the FokkerPlanck equation by adopting the effective field
method.281
With an exploration of nonlinear
perturbation techniques, Engel et al. admit that
only a particularly chosen Langevin function
Figure 51 Ferrofluid rotation (A) induced at a distance
yields the correct time-averaged z-component
from a static Hx field added to an oscillating Hy field (B)
of the torque Nz, with static and dynamic
magnetic field terms included. The expression for Nz shows that both the static magnetic field and the
anharmonic part of the oscillatory component are essential for the directed rotation to occur.
Interestingly, the Brownian relaxation time is another parameter which had to be heuristically
determined to achieve agreement between theory and experiment. It corresponded to a particle size of
approximately 35 nm which is about three times the average particle size. Engel et al. conclude that the
Brownian relaxation time must therefore correspond to the largest grains in the population rather than
the average.
Engel et al. succeeded in rectifying rotational Brownian motion angular momentum. It is an
experimental realization of “the combined action of many individual nanoscale ratchets to yield a
macroscopic thermal noise transport effect.”282
65
Rectifying Thermal Electric Noise
In regards to rectifying thermal electrical noise, it is worth mentioning the U.S. Patent
#3,890,161 by Charles M. Brown that utilizes an array of nanometer-sized metal-metal diodes, capable
of rectifying frequencies up to a terahertz (1012 Hz). Brown notes that thermal agitation electrical noise
(Johnson noise) behaves like an external signal and can be sorted or preferentially conducted in one
direction by a diode. The Johnson noise in the diode is also generated at the junction itself and
therefore, requires no minimum signal to initiate the conduction in one direction. The thermal noise
voltage is normally given by V2 = 4kBTRB where R is the device resistance and B is the bandwidth in
Hertz.283 Brown’s diodes also require no external power to operate, in contrast to the Yater diode
invention. Brown also indicates that heat is absorbed in the system, so that a cooling effect is noticed,
because heat (thermal noise) energy energizes the carriers in the first place and some of it is converted
into DC electricity. In contrast, the well-known Peltier effect is the closest electrothermal phenomenon
similar to this but requires a significant current flow into a junction of dissimilar metals in order to create
a cooling effect (or heating). Brown suggests that a million nickel-copper diodes formed in micropore
membranes, with sufficient numbers in series and parallel, can generate 10 microwatts. The large scale
yield is estimated to be several watts per square meter.
Quantum Brownian Nonthermal Recifiers without Ratchets
While many researchers believe that the asymmetrical ratchet of one form or another is
essential in the conversion of stochastic fluctuations, there are others who also find that stochastic
resonance (SR) in threshold systems is a sufficient substitute. “The ‘cooperation’ between the signal
and noise introduces coherence into the system…This coherence is conveniently quantified as the
power spectral density…of the system response…The earliest definition of SR was the maximum of the
output signal strength as a function of noise…”284 An introduction to SR is shown in Figure 52 with a
potential barrier Uo separating two wells at +c. If the energy is subthreshold, the system will be
monotonic but adding an amount of noise on the order of Uo allows the dichotomic system to oscillate.
With a supra-threshold periodic forcing, the two wells may have different net occupation levels (as
arrows indicate), with the output signal-to-noise ratio (SNR) following the input SNR closely.
Anomalous transport properties, using SR, which do not exploit the ratchet mechanism have
been investigated in driven periodic tight-binding (TB) lattices near zero DC bias with the combined
effects of DC and AC fields, or DC field and
external noise. In particular, Goychuk et al.
have found that periodic TB lattices can be
Figure 52 Bistable
driven by unbiased nonthermal noise
dichotomic potential
generated from the vacuum ZPF, generating
with periodic forcing
an electrical current as a result of a “ratchetlike
mechanism,” as long as there is quantum
dissipation in the system.285
Theoretically
introducing
quantum
dissipation with an ensemble multi-state model
of harmonic oscillators coupled to the driven
system, along with an unbaised, timedependent random force (characterized by an
external, time-dependent random electric field,
η(t) = eaEη(t)/h), yields the noise-averaged
stationary quantum DC electrical current Jst =
e(lim tÆ∞)d<q(t)>/dt and quantum diffusion
coefficient D. The nonthermal fluctuations are
given
discrete,
quantum
values
with
probabilities as QED dictates. It is assumed that
neither the temperature nor the nonthermal
66
fluctuations can cause any essential occupation of higher energy levels for the dissipation model.
Goychuk et al. succeed in demonstrating that without dissipation, for any field, the stationary DC
current is always zero. An initially localized particle, as in a crystal, does not produce a current in the
absence of dissipation. However, considering the effect of adding unbiased fluctuations η(t) on Bloch
oscillations, Goychuk develops a master equation which includes a real-time quantum Monte Carlo
calculation yielding a good approximation for a TB particle at environmental temperatures and/or strong
dissipation when transport includes
sequential tunneling. Bloch functions
describe an electron in a periodic lattice
with a sinusoidal wave function
conditioned by a lattice periodicity
function.286 Driven tunneling dynamics
in Bloch oscillation system is the subject
of another paper Goychuk has
coauthored with efficient determination
of the optimal control of quantum
coherence.287
In Figure 53, the production of
rectified electrical current Jst is shown
with an ohmic friction factor α = 1
graphed against changes in fluctuation
noise strength σ for a dichotomic (twochoiced) random process with zero
Figure 53 Stationary current versus noise strength for a
mean and asymmetry parameter of ξ
random process. Solid line is adiabatic approximation. Inset
= ½. While the solid line is adiabatic,
is current reversal with friction.
the dashed lines depict non-adiabatic
autocorrelation times of 0.1ωc and ωc
respectively from top down, where ωc is the cutoff frequency. The inset graph is an interesting current
reversal that occurs under a case of strong friction α = 5 which is related to SR. “Because the current
appears as the nonlinear response to the aperiodic external signal, the existence of this maximum [in
Figure 53] can be interpreted as a signature of aperiodic quantum stochastic resonance.”288
The stationary current is also found
to depend on temperature, which is the
signature
of
aperiodic
quantum
stochastic resonance (AQSR). In Figure
54, the rectified current is shown versus
temperature for a fluctuation noise
strength σ =0.5ωc (solid line) and σ = 7ωc
(dashed line) while friction α = 1 and
asymmetry ξ = 1.
In the presence of unbiased,
asymmetric forcing, a noise-directed
current always occurs in a dissipative TB
lattice, because of the ratchet-like effect of
the asymmetric forcing, like the stochastic
ratchets that rectify thermal
noise. With stochastic
resonance,
nonthermal
fluctuations are effectively rectified, creating a measurable current. Goychuk believes that the
effect should be already observable in superlattices and/or optical lattices.289
Figure 54 Aperiodic quantum stochastic resonance shown (dashed line
with noise σ = 7ωc ) with an insert of current reversal under strong friction.
67
For reference, it is worth mentioning that with crystal lattices, thermal fluctuations appear at
environmental temperatures, with ½ mωo2<u2> = 3(½kBT) energy level where m and ωo are the mass
and frequency of the harmonic oscillations and u is the displacement from a fixed lattice site. The
nonthermal oscillations associated with ZPE are mωo2<u2> = 3(½hωo) in terms of energy, adding to the
lattice thermal fluctuations.290
Zero Point Energy Corresponds to Dark Energy
While some may still question the availability of nonthermal fluctuations from the ZPF in a solid
state device, Beck and Mackey experimentally measured the spectral density of current noise in
Josephson junctions in 2004. They assert that it provides direct evidence for the existence of zero-point
fluctuations. Assuming that the total vacuum energy associated with these fluctuations cannot exceed
the presently measured dark energy of the universe, they predict an upper cutoff frequency of ηc =
(1.69 +/- 0.05) x 1012 Hz for the measured frequency spectrum of zero-point fluctuations in the
Josephson junction. This provides a reasonable resolution to one of the most hotly contested issues of
ZPE: its cutoff frequency. Note that it is significantly less than the Planck cutoff frequency of ωc ≈ 1043
Hz based on the Planck length discussed in Chapter 1. Furthermore, Beck and Mackey help explain
astronomy’s self-created dilemma of dark energy which has remained unresolved because of
misunderstandings of the properties of ZPE.291 The largest frequencies that have been reached in the
experiments are of the same order of magnitude as ηc and provide a lower bound on the dark energy
density of the universe. They show that suppressed zero-point fluctuations above a given cutoff
frequency can lead to 1/f noise. Therefore, it is quite conceivable that their experiment can measure
some of the properties of dark energy in the lab.292
Vacuum Field Amplification
With the introduction to AQSR along with the rectification of nonthermal noise, it makes sense to
investigate the amplification of quantum noise. Milonni points out that “the vacuum field may be
amplified…if the spontaneously emitted radiation inside the cavity is amplified by the gain medium, then
so to must the vacuum field entering the cavity. Another way to say this is that ‘quantum noise’ may be
amplified.”293 Since the SR TB lattice current output depends on the noise level, as in the Goychuk
simulation, the optimum level of energy extraction depends on parameter control, as in quantum optics,
which utilizes quantum noise amplification. This is similar to ASE which also uses a gain medium.
The actual content of quantum noise and vacuum polarization may still remain a mystery after
all of the Chapter 4 analysis. Milonni notes that even though heavier virtual particle pairs like muons,
pions, etc. may take part in virtual polarization, the majority of the manifested particles will always
be electron-positron pairs because of the 1/m2 mass dependence of the nonexchange term between
the two current densities for the electron and the negative-energy states of the ZPF.294 Jackson notes
that the Weisacker-Williams “method of virtual quanta” treats every scattering impact or close
encounter between charged particles as a Fourier collection of virtual particles which are equal to the
electric field pulse radiated to the target. This method, in consonance with QED, gives the frequency
spectrum, cutoff, and number of virtual particles per unit energy interval.295
68
CHAPTER 5 - Summary, Conclusions and Recommendations
Summary
This study was predicated on the existing volume of data already in the scientific literature
regarding the nonthermal vacuum fluctuations that comprise ZPE. The assessment of the feasibility of
zero-point energy extraction by humans from the quantum vacuum for the performance of useful work
in the electrical, fluidic, thermodynamic, and mechanical conversion modalities is determined in this
chapter.
Analyzing the specific experiments, theories, simulations, measurements and predictions in this
study offers a wealth of details concerning the energetic operation of ZPE throughout the universe. As
a result, it can possibly be argued from an historical perspective that, because nature already extracts
ZPE for the performance of useful work, humans eventually will be able to so as well. Acknowledging
the need for robust, concentrated energy sources in the world, any study of the concept of energy
extraction and production should address the corresponding utility and energy quality. Therefore, this
summary addresses the electrical power output and the practicality of the conversion mode and
method.
This study finds that at the present time, the categories of the present major inventive ZPE
conversion modes includes 1) electromagnetic conversion, 2) Casimir cavity mechanical engine, 3) fluid
dynamics techniques, and 4) quantum thermodynamic rectifiers. Under these major headings are
individual methods such as 1a) focusing vacuum fluctuations, 2a) cavity QED, 2b) spatial squeezing,
2c) Casimir cavity geometry design, 2d) Casimir stress enhancement, and 2e) vibrating cavity photon
emission, 3a) inertial effects, 3b) hydrodynamic model, 3c) Casimir cavity, 4a) quantum coherence, 4b)
Brownian motors, 4c) transient fluctuations, 4d) thermal fluctuation rectifiers, and 4e) nonthermal
Brownian rectifiers, as shown in Table 1 with relevant author names.
Table 1 - ZPE Conversion Modes & Methods
Electromagnetic
Dual sphere - Mead
Focusing
Ford
ZPE
Mechanical
Casimir engine Pinto
- Cavity
QED
Haroche
Spatial squeezingHu
Casimir
cavity
optimized design Maclay
Vibrating
cavity
photon emission Hizhnyakov
Fluid Dynamic
Inertia Effects Froning
Hydrodynamic
model – Bohm
Casimir cavity Maclay
Thermodynamic
Quantum coherence Allahverdyan, Scully
Brownian
motors
Astumian
Transient
fluctuation
theorem - Crooks
Thermal
fluctuation
rectifiers
–
Brown,
Ibarra-Bracamontes,
Engel
Quantum
Brownian
nonthermal rectifiers Goychuk
Electromagnetic Conversion
In the electromagnetic energy conversion process, the proposed Mead configuration of two
spheres in close proximity was analyzed for four different size categories, each of which are a thousand
times smaller than the previous one. The microsphere category seemed to match the Mead design
closely but was found to be lacking in sufficient scattering intensity, even when substituting conducting
69
spheres which have the highest scattering cross section. The decrease of dielectric constant with
frequency also was a problem for most materials. The ZPF energy density and resonant photon energy
for the microsphere were only moderate and are summarized in Table 2, along with the other three
spheres.
The nanosphere, as shown in Figures 16 and 17, demonstrates the present state of the art in
nanotechnology assembly. The spectral energy density of Equation (16) for the nanosphere increases
by a billion times over the microsphere even though the sphere size is reduced by a billion times. Upon
integrating over a decade of frequencies with Equation (21) (see Table 2), a thousand times increase in
ZPE density is calculated with each successively smaller sphere. However, no significant vacuum
polarization is available for nano-sized particles, which is an energetic, physical manifestation of ZPE.
The picosphere is interesting in that Mead’s beat frequency concept can theoretically be
realized with pairs of atoms very close in atomic weight such as platinum and gold or hydrogen and
deuterium. However, the engineering challenges of such an assembly would be prohibitive, even if one
could foresee a significant overunity energy production per pair. Furthermore, even with the advanced
techniques such as Ford’s focusing of vacuum fluctuations, textbook upscattering or resonant
fluorescence, etc., paired atoms of choice still have a technological barrier, lacking compatibility with
any existing amplification or conversion transducer, such as those seen in Figure 21.
With the femtosphere, QED principles inherent to ZPE, start to emerge. In one sense, the
femtosphere has become almost too small to manage individual particles, if they are in contact. In
another sense, the size presents other opportunities such as with the ion trap, where electron
femtospheres can be collected, for example. However, even as the advantage of working with electrons
as ZPE receivers becomes more apparent, it is obvious much more research is needed.
Overall, the Mead patented method for utilizing ZPE collectors and resonators certainly
presents a design or a collector that amplifies scattering, though Mead only analyzes a single sphere.
The ZPF energy density of Equation (21) is the most relevant, showing the quartic increase of energy
with frequency even though there is a cubic decrease of volume with each successive sphere. In the
final assessment, given the extent of the experimentation that is required for success with this concept
for extraction of useful energy, all four spheres of interest still do not receive a feasibility rating of
overall confidence that would qualify it for endorsement from scientists, engineers, or investors. Using
the realistic power production level or anticipated work output as a measure of energy quality, this
invention receives a poor energy quality rating.
Table 2 – Energy and Cross Section of the Spheres
Photon energy &
frequency
E = mc2
comparison
ZPE energy
density
Physical cross
section area
Scattering cross
section
Microsphere
1 eV
1014 Hz
Nanosphere
1keV
1017 Hz
Picosphere
1 MeV
1017 Hz
Femtosphere
1 GeV
1020 Hz
Si: 1044 eV
Ag: 1017 eV
Pt: 1011 eV
p: 940 MeV
390 meV/μm3
390 eV/nm3
390 keV/pm3
390 MeV/fm3
3 x 10-12 m2
3 x 10-18 m2
3 x 10-24 m2
3 x 10-30 m2
10-8 m2
10-15 m2
10-21 m2
10-30 m2
Table 2 presents more energy data for each sphere, with photon energy for the corresponding
wavelength and the Einstein energy content added for comparison. The main observation with this
tabular summary is that the ZPE energy for a given spherical volume finally equals (same order of
magnitude) the Einstein energy content of matter as well as the photon energy of the corresponding
wavelength. While the scattering cross section may seem to offer some advantages at larger sphere
70
diameters, the equal weighting of light, matter, and vacuum for a femtosphere has to be extraordinarily
inviting for the vacuum engineer and an area worthy of further research.
Mechanical Casimir Force Conversion
The Casimir force presents a fascinating exhibition of the power of the ZPF offering about one
atmosphere of pressure when plates are less than one micron apart. As is the case with magnetism
today, it has not been immediately obvious, until recently, how a directed Casimir force might be
cyclically controlled to do work. The optically-controlled vacuum energy transducer however, proposed
by Pinto, presents a powerful theoretical case for rapidly changing the Casimir force by a quantum
surface effect, excited by photons, to complete an engine cycle and transfer a few electrons. The
exciting part of Pinto’s invention is the QED rigor that he brings to the analysis, offering a convincing
argument for free energy production. The nano-fabrication task that is presented, however, is
overwhelming. Besides mounting nanolasers inside the Casimir cavity, the process suggests that a 10
Khz repetition rate is possible with a moving cantilever, without addressing the expected lifespan. The
energy production rate is predicted to be robust (0.5 nW per cell or 1 kW/m2), which could motivate a
dedicated research and development project in the future. However, the Casimir engine project of
Pinto’s appears to be a long-term, multi-million dollar investment at best.
Utilizing some of the latest cavity QED techniques, such as mirrors, resonant frequencies of the
cavity vs. the gas molecules, quantum coherence, vibrating cavity photon emission, rapid change of
refractive index, spatial squeezing, cantilever deflection enhancement by stress, and optimized Casimir
cavity geometry design, the Pinto invention may be improved substantially. The process of laser
irradiation of the cavity for example, needs to be replaced with one of the above-mentioned quantum
techniques for achieving the same variable Casimir force effect, with less hardware involved. At the
present stage of theoretical development, the Pinto device receives only a moderate rating of feasibility.
It’s energy quality rating, however, is very high.
Fluid Dynamics
In the fluid dynamics analysis of the vacuum presented by Froning, it was convincingly argued
that the permittivity and permeability of the vacuum can be reduced effectively by nonabelian
electromagnetic fields, specifically by utilizing alternating current toroids at resonant frequencies.
While this research does not directly produce electricity, the energy extraction indirectly
achieved by the use of the Froning prototype is in the form of energy conservation. By reducing the
drag and inertia normally experienced by a spaceship in space, it will save a significant amount of
energy, which is equivalent to generating it. The referenced information from Rueda and Haisch as well
as from Maclay supports the validity of Froning’s fluid dynamic approach. At its present stage of
development, the feasibility rating is low, with an energy quality rating of high.
Thermodynamic Conversion
The Photo-Carnot engine is an interesting theoretcial device that relies upon quantum
coherence to yield a cyclical radiation pressure for the piston-driven engine. The phase induced with
the quantum coherence, provides a new control parameter that can be varied to increase the
temperature of the radiation field and to extract work from a single heat bath. The claim is made that
the second law of thermodynamics is not violated, according to Scully et al., because the quantum
Carnot engine takes more energy, with microwave input, to create the quantum coherence than is
generated. However, it is possible that as efficiency improvements are made, the output will exceed the
input as is the trend with the other thermodynamic engines analyzed in this study. After all, depending
on the value of the phase Φ, the efficiency of the quantum Carnot engine can already exceed that of
the classical engine – even when Tc = Th. The capability of extracting heat from a single reservoir
should be regarded as a requirement for a ZPE thermodynamic transducer. With the added
endorsement of Allahverdyan and Nieuwenhuizen, the Photo-Carnot engine is rasied to a ‘perpetuum
mobile of the second kind.’ The number of cycles cannot be arbitrarily large apparently, and the total
amount of extractable work is modest. However, the standard requirements for a thermal bath are not
71
fulfilled, according to Allahverdyan and Nieuwenhuizen, so thermodynamics just does not apply. For
these reasons, the Photo-Carnot invention has great potential for becoming a ZPE energy producer
and receives a high feasibility rating, with moderate energy quality rating.
The Brownian motors proposed by Astumian (Figures 44) utilize Langevin’s equation, also
mentioned in connection with the quantum coherence of Scully et al. Astumian emphasizes the
fluctuating energy source (thermal noise) and the dissipation (viscous drag) that is essential to the
fluctuation-dissipation theorem, fundamentally important to the ZPF. With Astumian’s Brownian motors,
the oscillating potential also needs an asymmetrical ratchet to ensure one-way transport. The ratchet
concept, while very feasible and proven by two experiments, offers only a limited production of current
with underunity efficiency. Astumian notes that with the viscous drag of the solvent, all of the energy
gained by the ratchet steps is dissipated with an overall thermodynamic efficiency of less than 5%.296
The tunneling electron ratchet experiment performed by Linke et al., seen in Figures 45-46, is
an encouraging demonstration of the Brownian motor. Linke generates a maximum of 0.2 nA with about
a millivolt of source-drain rocking voltage, at the picowatt or picojoule level, which is encouraging.
However, with only between 1% and 5% rectification of the total current, the efficiency is also quite as
low as Astumian.
With the analysis of the transient fluctuation theorem, it becomes apparent that with microscopic
systems, the performance of negative work has a high probability, apparently violating the law of
entropy. The Metropolis Monte Carlo simulation of Crooks in Figure 48 is similar to the quantum ratchet
concept however, and doesn’t offer an advantage over the other techniques.
The Yater method for power conversion of energy fluctuations is in the same category as
rectifying thermal noise. While the Yater invention has an impressive assembly of patents and journal
articles, the process requires two heat sources separated by a large spread in temperature. This makes
the overall analysis of the device difficult to analyze except by conventional means with underunity
energy output projections. His claims for a 10 times improvement over heat pumps is intriguing and the
detailed plans in his patent encourage further research, with a reasonable feasibility projected and high
energy quality.
The work by Ibarra-Bracamontes et al. is another confirmation of rectifying thermal fluctuation
noise. It is interesting for theoretical analysis but the type of signals that are possible for external forcing
is not made clear. Rectifying random thermal fluctuations with ferrofluids adds a new twist that is
unique, especially when rotational energy is not available directly from the ZPF. Engel et al. offer a
fascinating experiment for consideration, consistent with the rectification of thermal fluctuations for
linear motion. However, the driving potential is a complex oscillating magnetic field with a field intensity
as high as the static field which is also required (several kA/m). Both are generated by a commercial
electromagnet. The work output that should be calculated in time-averaged torque multiplied by
rotational distance will predictably be only a few percent of the input, at best. It is a good demonstration
but does not seem to represent a practical concept for motoring or rotational work. Therefore, it
receives a high feasibility rating but low energy quality.
The Brown patent rectifying thermal electrical noise with nano-sized metal-metal diodes is
probably the most exciting invention analyzed in Chapter 4. Though the inventor does not acknowledge
a ZPE contribution to Johnson noise, it is reasonable to project that the Brown diode arrays will rectify
nonthermal fluctuations as well as thermal noise. With no external input needed for conduction, nor a
minimum voltage to overcome the usual diode barrier, the potential for free energy production seems
quite high. The attractiveness and projected consumer interest for such a solid state, zero-maintenance
device is also very high. Not only is the fabrication understandable and straightforward but the
description of a cooling effect (negative kinetic energy) from the conversion of thermal noise (positive
kinetic energy) is also scientifically and thermodynamically acceptable. The energy density of several
watts per square meter is reasonable and robust. However, this quantity should be calculated in watts
per cubic meter, since the filled Millipore sheets can easily be stacked vertically as well. Another
important calculated parameter for space power is the amount of watts per kilogram, which is probably
72
moderate to high in this case. It is possible with modern nanotechnology that this invention could
compete with the battery market. Not only is the feasibility given the highest rating for this invention, but
the energy quality rating is also given the highest rating as well.
Stochastic resonance is an emerging energy field that now is being used to substitute for
ratcheting in the Brownian rectifiers. The work by Goychuk demonstrates the aperiodic quantum
stochastic resonance (AQSR) that is essential for these rectifiers to work in a solid state environment of
a tight-binding crystal lattice. With near zero DC bias, the invention is very attractive for many reasons.
The “ratchetlike mechanism” of Goychuk is a valuable substitute for the Astumian style of Brownian
motor requiring physically fabricated ratchets. It does not require a static bias, which is a distinct
improvement over previously analyzed Brownian motor requirements. The stationary current is also
found to be nonzero for unbiased noise, demonstrating a DC rectification, as long as there is some
degree of asymmetry in the noise. As a result, the invention combines the noise and the asymmetric
driving force into one signal, which is also an advantage over lesser ZPE models. The AQSR design
has the ability to rectify asymmetric, unbiased, nonthermal noise, including quantum fluctuations as
well, producing a measurable electrical current in a solid state crystal lattice. The only remaining
variables are the amount of quantum dissipation required for the effect, the optimum operating
temperature, the anticipated energy efficiency and the projected difficulty inherent in creating
asymmetry with nonthermal noise that naturally tends to be symmetric in time and space. These
variables may be of a sufficiently minor concern for the Goychuk invention to actually offer a gateway to
the future of ZPE electricity generation. Many parts of the invention fit the ideal “impedance” matching
of energy source behavior with energy transducer behavior. For example, quantum fluctuations are
shown by Goychuk to simply require quantum dissipation and a slight asymmetry, which is less energy
intensive overall than creating a quantum coherence. This invention is given the highest rating for
feasibility and the highest rating for energy quality.
Conclusions
The risk analysis that is often integrated into a feasibility study that is dedicated to a single
development plan is really a process to assign a degree of likelihood to stages of a project.297 The
feasibility rating standard adopted in Chapter 5 is equivalent to such an analysis.
The results of this study finds varying feasibility ratings and energy quality ratings for the four
modes of energy conversion from the ZPF. For the Electromagnetic modality, in the present stage of
development, the overall method is rated unfeasible with poor energy quality, given the limitations of
today’s technology capabilities. The Mechanical modality fares better with a moderate feasibility rating,
at the overall present stage of development, with a very high energy quality rating. The Fluid Dynamic
modality drops back with a low feasibility rating but high energy quality rating. The Thermodynamic
modality shines with the highest feasibility rating and the highest energy quality rating.
The overall conclusions drawn from this study support the introductory physical description of
the quantum vacuum. Furthermore, the hypothesis of a ZPF vibrating with measurable mechanical
pressure, electromagnetic activity, and nonthermal energy is also supported by the scientific evidence
uncovered by this study. The fluid dynamics information about ZPE was a reassuring fulfillment of the
fourfold modality expectation. There is also a consistency with previous research going back to the
early days of QED, which adds a reliability and confidence level to the normally unsettling nature of
ZPE. Further research is needed however, as outlined briefly in the next section, to fully exploit the
discoveries of energy extraction from the quantum vacuum.
The implications of this study to the emerging field of discipline called vacuum engineering are
enormous and far-reaching: An up-to-date assessment of the state of the art has been accomplished by
this comprehensive study. Based on this engineering physics achievement, with the feasibility
and energy quality ratings therein, it can be reasonably expected that at least one business plan
will be generated for a ZPE invention, perhaps for the first time in history. Such a development
offers the business world an opportunity to benefit from the most plentiful energy source that also now
has been found to have a certain level of practicality and moderate risk assessment, compatible with
73
competing enterprises. As a result of this study, an opportunity has emerged for the public to benefit
from some of the ZPE unusual ubiquitous qualities, such as making many completed ZPE transducers
completely portable and possibly installing lifetime ZPE transducers in every appliance. The
implications of this study are that future generations may finally relinquish fossil fuels in favor
of ZPE.
Recommendations
Based on the quality of research uncovered and the level of agreement between theory and
experiment demonstrated, specifically by the thermodynamic mode of ZPE conversion, it is
recommended that further attention and funding be primarily dedicated to the exploitation of zero-point
energy extraction, beginning with the microscopic realm. While the other three modalities offer
interesting and promising developments, the feasibility rating and energy quality rating is the highest
with the thermodynamic mode. In particular, it is recommended that 1) metal-metal nanodiodes
should be researched, with attention to the Johnson noise voltage and purported lack of diode barrier,
along with the possible mass production of high density substrates; 2) more ratchet and ratchetlike
asymmetries should be researched, by government, industry and academia, so that a TB lattice or
diode assembly may one day offer a truly solid state transducer for ZPE; 3) research should continue
into quantum coherence, refractive index change, and stochastic resonance with a goal of
reducing the present relatively large energy investment, so that more robust avenues of product
development in ZPE thermodynamics may be achieved. Brownian motors, thermal fluctuation rectifiers,
and quantum Brownian nonthermal rectifiers utilizing AQSR have already achieved a level of theoretical
and experimental confidence where further physics research and engineering studies can offer fruitful
rewards in the production of rectified DC electricity. This mode of ZPE conversion research and
development needs to be continued with earnest in order to expand mankind’s woefully limited portfolio
of energy choices.
A broad outline of how to undertake the recommended development work would include
specific tasks and milestones associated with a) the confirmation of ZPE quantum effects
described in this study on a larger scale; b) replication of results but also optimization of
results; and c) engineering tasks of conductor and semiconductor design, nanowires and ohmic
contacts. All of these, along with other tasks not mentioned, need to be included. The project would
also include estimates of output current and energy production with any given geometry. Parallel
development paths in research and development will always accelerate the completion of the optimum
design. A market study should also accompany the work, so a clear focus on the existing niche to be
filled is maintained. A national or international project proposal that estimates the required project
scope, resources, break-even point and identifies major milestones, has to be formulated, if major
progress in ZPE usage is to be achieved. Simply commissioning another study to follow up this study
will lead only to institutionalizing the effort without accomplishment of set goals.
This feasibility study of ZPE extraction for useful work has presented a balanced and detailed
assessment with scientific integrity, engineering utility and the likelihood of success for further
development. It can be concluded that zero-point energy is deserving of more attention by
engineers and entrepreneurs as a serious and practical energy source for the near future. The
proposed project plan for ZPE development, yet to be written, has been reduced to a business
endeavor and an exercise in return on investment.
74
Table 3 - Vacuum Engineer’s Toolkit
Tool
Effect
Page
Aperiodic quantum stochastic
resonance (AQSR)
Generates electrical current from nonthermal and thermal fluctuations
65-67
Brownian motors
Casimir engine
Biases Brownian motion of particles, often in an anisotropic medium
Electrical current generator designed by Pinto using a microcantilever,
microlaser and Casimir force
58
44-47
Casimir force
Attractive (or repulsive) force from two parallel plates about 1 micron apart
6, 18, 50
Cavity QED
Dark energy
Dielectric constant of surface
Einstein-Hopf drag
Electromagnetic ZPE Converter
Femtosphere
Fluctuation-Dissipation theorem
Alters atomic transition probability in small cavities
ZPE that powers galactic acceleration, also measured in the lab
Affects Casimir force when illuminated by light
Retarding force from vacuum due to motion F= -Rv
Dual sphere device using beat frequencies to downshift ZPE
Particle size where QM and Rutherford scattering applies
Source+dissipation=fluctuation; Predicts and explains fundamental nature
of ZPF
20
67
45, 52, 53
55
27-44
40-44
11, 57
Fluctuation-driven transport
mechanism that can convert chemical energy into motion of particles and
macromolecules
58
Focusing vacuum fluctuations
Fokker-Planck equation
Increases energy density of ZPE and attractive Casimir force
Can apply to ferrofluid system to predict noise-driven motion of particles
48-49
64
Langevin's equation
Lasing without inversion (LWI)
Like F-D theorem, helps design Brownian motors
Sustained laser output from microlasers which have long radiation cavity
lifetime
58, 63
56
Magnetic field
Microbox geometry
Microcantilever
Microlaser
Nonresonant ion trap
Photo-Carnot engine
Inhibits Casimir force
Varies Casimir force from + attractive to - repulsive
Flexible membrane that displays Casimir deflection
Solid state laser 2 microns across
Electrfied cavity that concentrates charged particles
Allows extraction of work from a single thermal reservoir where radiation
is the working fluid
20
50-51
44, 49
46
44
56
Quantum coherence
Quantum ratchet
Recoil
Changes relative strengths of emission and absorption in a cavity
Repeating cells that move particles with fluctuation-driven transport
Increases the energy of a dipole, associated with photon absorption and
emission, both of which are in the same direction
57
59-60
55
Rectifying thermal noise
Resonance
Resonant fluorescence
Generates electrical current with asymmetric external potential
Can trap scattering particles into bound state
Dramatically increases absorption when incident energy equals binding
energy of target
64
42
41
Sonoluminescence
Spatial squeezing of vacuum
ZPE caused light emission due to extreme temperature and pressure
Can double photon emission from cavity by changing dimensions abruptly
21
48
Temperature
Thermal fluctuations/noise
Time-dependent refractive index
Transient fluctuation theorem
Unruh-Davies Effect
Upscattering
Vacuum field amplification
Vacuum field perturbations
Vacuum polarization
Increase will broaden resonance peak
temperature-caused stochastic oscillations and vibrations
Causes part of ZPE to convert to real photons
Nonzero probability for negative work for short periods of time
Acceleration causes ZPE to create thermal fluctuations
Gain of energy to incident particle up to 10 kT energy
Increases quantum nonthermal noise with a gain medium
Nonabelian EM field may alter speed of light/object
Increase in local activity in the quantum vacuum near the edge of a
physical charged particle
* This page may be freely copied and distributed with acknowledgment of source *
Practical Conversion of Zero-Point Energy: Feasibility Study, Revised Edition 2005 by
Thomas Valone PhD, PE
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62-63
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61
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2009 Update: Download for free the latest zero point energy journal article
by the author, http://www.integrityresearchinstitute.org/
ZeroBiasDiodeArrays-Valone-SPESIF2009.pdf
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FIGURE CREDITS
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17. Ibid., p. 1485
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20. Snow, T. P. and J. M. Shull. Physics, West Pub. Co., St. Paul, 1986, p. 744
21. Fink, p. 10-42
22. “Electromagnetic Spectrum” TRW, Inc., Electronics Systems Group, Redondo Beach, CA, October, 1986
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24. Duderstadt, James and L.. Hamilton, Nuclear Reactor Analysis, J. Wiley & Sons, New York, 1976, p. 54
25. Ibid., p. 49
26. Jackson, p. 803
27. Baym, Gordon. Lectures on Quantum Mechanics. Benjamin/Cummings, Reading, 1978, p. 211
77
28. Brink, G. O., “Nonresonant Ion Trap” Review of Scientific Instruments, Vol. 46, No. 6, June, 1975, p. 739
29. Ibid., p. 740
30. Pinto, F. “Engine cycle of an optically controlled vacuum energy transducer” Phys, Rev. B, Vol. 60, No. 21,
1999, p. 14745
31. Ibid., p. 14746
32. Gourley, P. “Nanolasers” Scientific American, March, 1998, p. 57
33. Dodonov, V.V. “Squeezing and photon distribution in a vibrating cavity” ” J. Phys. A: Math Gen. V. 32, 1999, p.
6720
34. Ford, L.H. et al. “Focusing Vacuum Fluctuations” Casimir Forces Workshop: Recent Developments in
Experiment and Theory, Harvard University, November 14-16, 2002, p. 19
35. Zheng, M-S., et al. “Influence of combination of Casimir force and residual stress on the behaviour of microand nano-electromechanical systems” Chinese Physics Letters, V. 19, No. 6, 2002, p. 832
36. Maclay, J. “Unusual properties of conductive rectangular cavities in the zero point electromagnetic field:
resolving Forward’s Casimir energy extraction cycle paradox” Proceedings of Space Technology and
Applications International Forum (STAIF), Albuquerque, NM, January, 1999, Figure 1, p. 3
37. Ibid., Figure 2, p. 4
38. Sagan, Carl. Cosmos, Random House, New York, 1980, p. 37
39. Froning, H.D. and R.L. Roach “Preliminary simulations of vehicle interactions with the quantum vacuum by fluid
dynamic approximations” Proceedings of 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, July,
2002, AIAA-2002-3925, p. 52236
40. Ibid., p. 52237
41. Ibid., p. 52239
42. Scully, M.O. et al. “Extracting work from a single heat bath via vanishing quantum coherence” Science, Vol.
299, Issue 5608, 2003, Figure 1, p. 862
43. Ibid., Figure 2, p. 865
44. Astumian, R. D. “Thermodynamics and Kinetics of a Brownian Motor” Science, Vol. 276, Issue 5314, Figure 3,
p. 919
45. Linke, H. et al. “Experimental Tunneling Ratchets” Science, Vol. 286, Issue 5448, 1999, Figure 1, p. 2314
46. Ibid., Figure 3, p. 2317
47. Blau, S. “The Unusual Thermodynamics of Microscopic Systems” Physics Today, September, 2002, Figure 1,
p. 19
48. Crooks, G.E. “Entropy production fluctuation theorem and the nonequilibrium work relation for free energy
differences” Physical Review E, Vol. 60, No. 3, September, 1999, p. 2724
49. Yater, J.C. “Relation of the second law of thermodynamics to the power conversion of energy fluctuations”
Physical Review A, Vol. 20, No. 4, October, 1979, Figure 1, p. 1614
50. Ibarra-Bracamontes, et al. “Stochastic ratchets with colored thermal noise” Physical Review E, Vol. 56, No. 4,
October, 1997, Figure 2A, p. 4050
78
51. Engel, A., et al. “Ferrofluids as Thermal Ratchets” Physical Review Letters, Vol. 91, No. 6, 2003, Figure 2, p.
060602-3
52. Bulsara, A.R. et al. “Tuning in to Noise” Physics Today, March, 1996, p. 39
53. Goychuk, I. et al. “Nonadiabatic quantum Brownian rectifiers” Physical Review Letters, Vol. 81, No. 3, 1998,
Figure 1, p. 651
54. Ibid., Figure 2, p. 651
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147
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149
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150
Jackson, p. 417
151
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152
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153
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154
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155
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156
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157
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158
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159
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86
160
Snow et al., p. 744
161
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162
Ibid., p. 2139
163
Metz, Clyde R. Schaum’s Outline Series: Theory and Problems of Physical Chemistry, 2nd edition, McGrawHill, New York, 1989, p. 435
164
Milonni, p. 84
165
Fink, p. 10-42
166
“Electromagnetic Spectrum” TRW, Inc., Electronics Systems Group, Redondo Beach, CA, October, 1986
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168
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169
Jackson, p. 644
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172
Duderstadt, James and L.. Hamilton, Nuclear Reactor Analysis, J. Wiley & Sons, New York, 1976, p. 53
173
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174
Duderstadt, p. 49
175
“Table of Periodic Properties of the Elements,” Side 2
176
Jackson, p. 682
177
Ibid., p. 627
178
Ibid., p. 647
179
Gautreau et al., p. 77
180
Jackson, p. 646
181
Feynman, Vol. I, p. 1-1
182
Jackson, p. 803
183
Ibid., p. 681
184
Schiff, p. 457
185
Baym, p. 211
87
186
Schiff, p. 457
187
Tipler, p. 438
188
Schiff, p. 125
189
Ibid., p. 126
190
Mittleman, Dehmelt, and Kim “Cold Kilo-Electron Ball as Probe for Charge-Proportional Cyclotron Frequency
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192
Milonni, p. 85
193
Ibid., p. 81
194
Brink, G. O., “Nonresonant Ion Trap” Review of Scientific Instruments, Vol. 46, No. 6, June, 1975, p. 739
195
Weisskopf, p. 310
196
Pinto, F. “Engine cycle of an optically controlled vacuum energy transducer” Physical Review B, Vol. 60, No.
21, 1999, p. 14740
197
Milonni, p. 221
198
Haroche, p. 57
199
Pinto, p. 14748
200
Ibid., p. 14743
201
Ibid., p.14743
202
Ibid., p. 14742
203
Ibid., p. 14744
204
Ibid., p. 14752
205
Falomir, H., et al. Divergencies in the Casimir energy for a medium with realistic ultraviolet behaviour” J. Phys.
A Math. Gen. V. 34, August 17, 2001, p. 6291
206
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Recent Developments in Experiment and Theory, Harvard University, November 14-16, 2002, p.1
207
An, K., et al. “Single-atom laser” Physical Review Letters, Vol. 73, 1994, p. 3375
208
Liu, Z. et al. “Virtual-photon tunnel effect and quantum noise in a one-atom micromaser” Physics Letters A, V.
217, 1996, p. 219
209
Pinto, p. 14750
210
Ibid., p. 14746
88
211
Cheng, H. “The Casimir energy for a rectangular cavity at finite temperature” J. Phys. A: Math Gen. Vol. 35,
March 8, 2002, p. 2205
212
Klimchitskaya, G. “Problems with the Thermal Casimir Force between Real Metals” Casimir Forces Workshop:
Recent Developments in Experiment and Theory, Harvard University, November 14-16, 2002, p.1
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Milonni, p. 187
214
Haroche, S. et al., p. 54
215
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9835
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Horoche, S., p. 60
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Weigert, p. 215
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Hu, Z. et al. “Squeezed Phonon States: Modulating Quantum Fluctuations of Atomic Displacements” Phys.
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Wiegert, p. 217
221
Weigert, p. 219
222
Dodonov, V.V. et al. “Squeezing and photon distribution in a vibrating cavity” J. Phys. A: Math Gen. V. 32,
1999, p. 6721
223
Ford, L.H. et al. “Focusing Vacuum Fluctuations” Casimir Forces Workshop: Recent Developments in
Experiment and Theory, Harvard University, November 14-16, 2002, p. 1
224
Ibid., p. 19
225
Milonni, p. 200
226
Zheng, M-S., et al. “Influence of combination of Casimir force and residual stress on the behaviour of microand nano-electromechanical systems” Chinese Physics Letters, V. 19, No. 6, 2002, p. 832
227
Lapedes, p. 754
228
Sperry, M. et al. “The role of the Casimir effect in the static deflection and stiction of membrane strips in
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229
Zheng, et al., p. 834
230
Milonni, p. 58
231
Ibid., p. 97
232
Ibid., p. 219
89
233
Maclay, J. “Unusual properties of conductive rectangular cavities in the zero point electromagnetic field:
resolving Forward’s Casimir energy extraction cycle paradox” Proceedings of Space Technology and Applications
International Forum (STAIF), Albuquerque, NM, January, 1999, p. 3
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Milonni, P.W. “Photon Steam Engines” Physics World, April, 2003, p. 2
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Ibid., p. 060602-2
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Ibid., p. 060602-4
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Goychuk, et al., p. 651
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Milonni, p. 30
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Ibid., p. 198
294
Ibid., p. 417
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Jackson, p. 724
296
Astumian, p. 923
297
Stevens et al., p. 37